% def.tex
%				Predrag			17feb2004
%				Predrag			 4oct2003
%				Predrag			30aug2003
%				Predrag			20jun2003
% 	   			Predrag  		17jan2003
% 	   			Predrag  		 6dec2002
% 	   			Predrag  		 7jul2002
% 	   			Predrag  		19nov2000
% 	   			Ronnie  		23sep2000
% Predrag disabled \basedirectory machine identifier 	25aug2000
% created   			Predrag  		30/10-94
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% define abreviations used throughout DasBuch
%% goal: make it easier to change conventions throughout
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%% WHERE ARE WE? %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% OPTIMAL:
% input a single line file that tells you where you are texing at
%
%       \providecommand{\basedirectory}{ronnie\@felix/asc/book/}
%
% or something like it.  Put this file outside the book subdirectory, in
% your own TEXINPUTS path, so when you ftp things back and forth
% the basedirectory.tex file will remain unchanged on each machine.
% then uncomment
%\input{basedirectory}
%
% MACHINE BLIND VERSION:
%
\providecommand{\basedirectory}{}
% \providecommand{\basedirectory}{{$\sim$}DasBuch/book/}
%

%%%%%%%%%%%%%%%%%%%%%% QUOTATIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  the learned/witty quotes at the chapter and section headings
% 
\newsavebox{\bartName}
\newcommand{\bauthor}[1]{\sbox{\bartName}{\parbox{\textwidth}{\vspace*{0.8ex}
	   %\hspace*{\fill}
	   \small\noindent #1}}}
\newenvironment{bartlett}{\hfill\begin{minipage}[t]{0.65\textwidth}\small}%
{\hspace*{\fill}\nolinebreak[1]\usebox{\bartName}\vspace*{1ex}\end{minipage}}

%
%  a quotation inserted into the text
%
\newenvironment{txtquote}{\begin{quotation} \small}{\end{quotation}}


%%%%%%%%%%%%%%%%%%%%%% INDEXING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\indx}[1] {#1\index{#1}}	% do not need to repeat the word


%%%%%%%%%%%%%%% PAGE STYLE (to write footers) %%%%%%%%%%%%%%%%%%%%%%%%%%%
\makeatletter
\newcommand{\inputfile}{ } 	% the rest is in the prlabels.sty
\newcommand{\version}{}


%%%%%%%%%%%%%%% PREPARE PAGINATION FOR bin/mkbook %%%%%%%%%%%%%%%%%%%%%%%
\newcounter{startSect}  %% page numbering used to generate ps pages
\newcounter{endSect}    %% page numbering used to generate ps pages
\newcommand{\chapName}{Unnamed} %% chapter label
\newcommand{\Chapter}[3]{\clearpage\thispagestyle{empty}\cleardoublepage
                \renewcommand{\inputfile}{#1 -  #2}
                         \renewcommand{\chapName}{#1}
                         \chapter[#3]{\textsf{\textbf{#3}}}
                         \label{c-#1}
                         \setcounter{startSect}{\thepage}
                        }
\newcommand{\References}[2]{\renewcommand{\inputfile}{#1 -  #2}
            %\renewcommand{\chapName}{#1} 	% do not rename the chapter
            %\setcounter{startSect}{\thepage}	% do not restart counting
	    \markright{\MakeUppercase{References}}
            \addtocontents{toc}{{\em references \thepage\ -}}
                        }
\newcommand{\Problems}[2]{\clearpage
                \renewcommand{\inputfile}{#1 -  #2}
                         \renewcommand{\chapName}{#1}
                         \setcounter{startSect}{\thepage}
			 \markright{\MakeUppercase{Exercises}}
			 \section*{\textsf{\textbf{Exercises}}}
			 %\addcontentsline{toc}{section}{{~~~~Exercises}}
                         \addtocontents{toc}{
                            {\em exercises \thepage \par}
					    }
                        }
\newcommand{\Solution}[3]{
		\section*{Chapter~\ref{c-#1}} 
                \renewcommand{\inputfile}{#2 -  #3}
		% PC:  modified 28 may 2000
                %         \renewcommand{\chapName}{#1}
                %        \setcounter{startSect}{\thepage}
                        }
\newcommand{\Solutions}{
		\section{\textsf{\textbf{Solutions}}}
		%\addcontentsline{toc}{section}{{~~~~Solutions}}
                        }
\newcommand{\Resume}{
		\section*{\textsf{\textbf{R\'esum\'e}}}
	%	\addcontentsline{toc}{section}{{~~~~Resum\'e}}
                \addtocontents{toc}{{\em  resum\'e \thepage\ - }}
                    }
\newcommand{\Remarks}{
		\section*{\textsf{\textbf{Commentary}}}
		%\section*{Historical remarks}
		\addcontentsline{toc}{subsection}{{~~~~Historical remarks}}
                        }
\newcommand{\forMkbook}{\setcounter{endSect}{\thepage}
                        \addtocounter{endSect}{-1}
\typeout{ set Chp=\chapName\space set pp=\arabic{startSect}-\arabic{endSect}}
\typeout{ dvips -q -pp $pp book.dvi -o $sdir/$Chp.ps ; echo finished $Chp}
\typeout{ $PS2PAGES $PS2PFLAGS $sdir/$Chp.ps > $sdir/$Chp-2p.ps ; echo finished $Chp-2p}
                         }

%%%%%%%%%%%%%%%%%%%%%% SPLIT ChaosBook.ps INTO VOLUMES %%%%%%%%%%%%%%%%%%%
\newcounter{startVol}   %% page number of the start of a volume 
\newcounter{endVol}     %% page number of the end of a volume
% \setcounter{endVol}{1} %% mess with this to renumber the stqrt v vol II
\ifthenelse{\boolean{prepare_pdf}}
	   {
	   \newcommand{\Volume}[2]{
%			 \setcounter{page}{\endVol} %experimenting
                         \addtocontents{toc}{
                                \vspace{18pt}
                                \hrule
                                \vspace{4pt}
                                \noindent
                                {\Large\textsf{\textbf{Volume~#1: #2}}}
                                \vspace{4pt}
                                \hrule
                                \vspace{12pt}
					    }
	                           }
%   \setcounter{page}{\value{endVol}}	% experimenting with hopping page nos
%   \addtocounter{page}{-22}	% experimenting with hooping page nos
	   \newcommand{\VolumeEnd}{\newpage }
           }{
				   %% prepare for postscript printing:
%RM	   \newcounter{startVol}   %% page number of the start of a volume 
%RM	   \newcounter{endVol}     %% page number of the end of a volume
	   \newcommand{\volName}{Unnamed} %% volume label
	   \newcommand{\Volume}[2]{
                         \renewcommand{\volName}{ChaosBook-#1}
%			 \setcounter{page}{\endVol} % experimenting 
                         \setcounter{startVol}{\thepage}
                         \addtocontents{toc}{
                                \vspace{18pt}
                                \hrule
                                \vspace{4pt}
                                \noindent
                                {\Large\textsf{\textbf{Volume~#1: #2}}}
                                \vspace{4pt}
                                \hrule
                                \vspace{12pt}
					    }
                                  }
\newcommand{\VolumeEnd}{
\setcounter{endVol}{\thepage}
\addtocounter{endVol}{-1}
\newpage
\typeout{ set Vlm=\volName\space set pp=\arabic{startVol}-\arabic{endVol}}
\typeout{ dvips -q -pp $pp book.dvi -o $sdir/$Vlm.ps ; echo finished $Vlm}
\typeout{ $PS2PAGES $PS2PFLAGS $sdir/$Vlm.ps > $sdir/$Vlm-2p.ps ; echo finished $Vlm-2p}
                         }
	   }  %end of ifthenelse prepare_pdf}


%%%%%%%%%%%%%%%%%%%%%% COMMENTS IN THE TEXT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% also search the text for lines starting with %%  to
% locate various internal comments, recent edits etc.
\ifthenelse{\boolean{display_comments}}
{ % if display_comments {true}, display comments in text
  \printlabels            %% turns on labeling of equations on margins
  \usepackage{showidx}    %% display index entries on margins

	\newcommand{\Preliminary}[1]
{\marginpar{\color{magenta}$\Downarrow$\footnotesize PRELIMINARY}%
{\color{magenta}#1}%
\marginpar{\color{magenta}$\Uparrow$\footnotesize PRELIMINARY}}

	\newcommand{\PublicPrivate}[2]
{\marginpar{\color{blue}$\Downarrow$\footnotesize PRIVATE}%
{\color{blue}#2}%
\marginpar{\color{blue}$\Uparrow$\footnotesize PRIVATE}}

	\newcommand{\PC}[1]
{\marginpar{\renewcommand{\baselinestretch}{0.7}\footnotesize #1}%
\renewcommand{\baselinestretch}{1.0}}
	\newcommand{\RM}[1]{\marginpar{
		\renewcommand{\baselinestretch}{0.7}
		\hrule \vspace{0.2ex}
		\footnotesize RM:~ #1
		\\ \hrule}%
		\renewcommand{\baselinestretch}{1.0}%
			        }
  \newcommand{\AW}[1]{\marginpar{
		\renewcommand{\baselinestretch}{0.7}
		\hrule \vspace{0.2ex}
		\footnotesize AW:~ #1
		\\ \hrule}%
		\renewcommand{\baselinestretch}{1.0}%
				}
  \newcommand{\LR}[1]{\marginpar{
		\renewcommand{\baselinestretch}{0.7}
		\hrule \vspace{0.2ex}
		\footnotesize LR:~ #1
		\\ \hrule}%
		\renewcommand{\baselinestretch}{1.0}%
				}
  %\newcommand{\LR}[1]{$\footnotemark\footnotetext{Lamberto: #1}$}
  \newcommand{\RA}[1]{$\footnotemark\footnotetext{Artuso: #1}$}
  \newcommand{\VB}[1]{$\footnotemark\footnotetext{Baladi: #1}$}
  \newcommand{\OB}[1]{$\footnotemark\footnotetext{Biham: #1}$}
  \newcommand{\PD}[1]{$\footnotemark\footnotetext{Dahlqvist: #1}$}
  \newcommand{\CPD}[1]{$\footnotemark\footnotetext{Carl: #1}$}
  \newcommand{\DJD}[1]{$\footnotemark\footnotetext{Driebe: #1}$}
  \newcommand{\AG}[1]{$\footnotemark\footnotetext{Garg: #1}$}
  \newcommand{\DG}[1]{$\footnotemark\footnotetext{Dorte: #1}$}
  \newcommand{\KTH}[1]{$\footnotemark\footnotetext{Kai H: #1}$}
  \newcommand{\BL}[1]{$\footnotemark\footnotetext{Lautrup: #1}$}
  \newcommand{\SFN}[1]{$\footnotemark\footnotetext{Sune: #1}$}
  \newcommand{\PER}[1]{$\footnotemark\footnotetext{Rosenqvist: #1}$}
  \newcommand{\HHR}[1]{$\footnotemark\footnotetext{HHR: #1}$}
  \newcommand{\EAS}[1]{$\footnotemark\footnotetext{Spiegel: #1}$}
  \newcommand{\NS}[1]{$\footnotemark\footnotetext{Niels S: #1}$}
  \newcommand{\GT}[1]{$\footnotemark\footnotetext{Tanner: #1}$}
  \newcommand{\GV}[1]{$\footnotemark\footnotetext{Vattay: #1}$}
  \newcommand{\DV}[1]{$\footnotemark\footnotetext{Divikar: #1}$}
  \newcommand{\NW}[1]{$\footnotemark\footnotetext{Whelan: #1}$}
  \newcommand{\DW}[1]{$\footnotemark\footnotetext{Wojcik: #1}$}
  \newcommand{\MAP}[1]{$\footnotemark\footnotetext{Mason: #1}$}
  \newcommand{\TB}[1]{$\footnotemark\footnotetext{Bartsch: #1}$}
}{	% if display_comments {false}, drop comments 
	% do not turn on labeling of equations on margins
  \newcommand{\Preliminary}[1]{}
  \newcommand{\PublicPrivate}[2]{#1}
  \newcommand{\PC}[1]{}
  \newcommand{\RM}[1]{}
  \newcommand{\OB}[1]{}
  \newcommand{\DG}[1]{}
  \newcommand{\GV}[1]{}
  \newcommand{\AG}[1]{}
  \newcommand{\VB}[1]{}
  \newcommand{\LR}[1]{}
  \newcommand{\PER}[1]{}
  \newcommand{\GT}[1]{}
  \newcommand{\AW}[1]{}
  \newcommand{\DW}[1]{}
  \newcommand{\PD}[1]{}
  \newcommand{\NS}[1]{}
  \newcommand{\RA}[1]{}
  \newcommand{\HHR}[1]{}
  \newcommand{\EAS}[1]{}
  \newcommand{\NW}[1]{}
  \newcommand{\KTH}[1]{}
  \newcommand{\CPD}[1]{}
  \newcommand{\DJD}[1]{}
  \newcommand{\BL}[1]{}
  \newcommand{\SFN}[1]{}
  \newcommand{\DV}[1]{}
  \newcommand{\MAP}[1]{}
  \newcommand{\TB}[1]{}
}
%%%%%%%%%%%%%%%%%%%%%% END OF ON/OFF COMMENTS SWITCH %%%%%%%%%%%%%%%%%%%%

\newcommand{\authorRA}%{\marginpar{RM+PC}}
         {\hfill (R. Artuso)}
\newcommand{\authorRAPC} %{\marginpar{EAS+PC}}
	 {\hfill (R. Artuso and P. Cvitanovi\'c)}
\newcommand{\authorOBPC} %{\marginpar{EAS+PC}}
	 {\hfill (O. Biham and P. Cvitanovi\'c)}
\newcommand{\authorOBCCPC} %{\marginpar{EAS+PC}}
	 {\hfill (O. Biham, C. Chandre and P. Cvitanovi\'c)}
\newcommand{\authorCCPSFKD} %{\marginpar{EAS+PC}}
	 {\hfill (C. Chandre, F.K. Diakonos and P. Schmelcher)}
\newcommand{\authorHHR} %{\marginpar{EAS+PC}}
	 {\hfill (H.H. Rugh)}
\newcommand{\authorRAHHRPC} %{\marginpar{EAS+PC}}
	 {\hfill (R. Artuso, H.H. Rugh and P. Cvitanovi\'c)}
\newcommand{\authorJMPC} %{\marginpar{EAS+PC}}
	 {\hfill (J. Mathiesen and P. Cvitanovi\'c)}
\newcommand{\authorGSPC} %{\marginpar{EAS+PC}}
	 {\hfill (G. Simon and P. Cvitanovi\'c)}
\newcommand{\authorRAPD} %{\marginpar{EAS+PD}}
	 {\hfill (R. Artuso and P. Dahlqvist)}
\newcommand{\authorRAPDGTPC} %{\marginpar{EAS+PD}}
	 {\hfill (R. Artuso, P. Dahlqvist, G. Tanner and P. Cvitanovi\'c)}
\newcommand{\authorPCRALREAS}
	 {\hfill (P. Cvitanovi\'c, R. Artuso, L. Rondoni, and  E.A. Spiegel)}
\newcommand{\authorPC} %{\marginpar{GV+PC}}
	 {\hfill (P. Cvitanovi\'c)}
\newcommand{\authorPD} %{\marginpar{PD+PC}}
	 {\hfill (P. Dahlqvist)}
\newcommand{\authorEASPC} %{\marginpar{EAS+PC}}
	 {\hfill (E.A. Spiegel and P. Cvitanovi\'c)}
\newcommand{\authorRMPCEAS}
	 {\hfill (R. Mainieri, P. Cvitanovi\'c and  E.A. Spiegel)}
\newcommand{\authorRM} %{\marginpar{RM+PC}}
	 {\hfill (R. Mainieri)}
\newcommand{\authorRMPC} %{\marginpar{RM+PC}}
	 {\hfill (R. Mainieri and P. Cvitanovi\'c)}
\newcommand{\authorFC} %{\marginpar{FC}}
	 {\hfill (F. Christiansen)}
\newcommand{\authorLRPC} %{\marginpar{LR+PC}}
	 {\hfill (L. Rondoni and P. Cvitanovi\'c)}
\newcommand{\authorLR} %{\marginpar{LR}}
	 {\hfill (L. Rondoni)}
\newcommand{\authorCPDPC} %{\marginpar{CPD+PC}}
	 {\hfill  (C.P. Dettmann and P. Cvitanovi\'c)}
\newcommand{\authorKTHPC} %{\marginpar{KTH+PC}}
	 {\hfill  (K.T. Hansen and P. Cvitanovi\'c)}
\newcommand{\authorGT} %{\marginpar{GT}}
	 {\hfill  (G. Tanner)}
\newcommand{\authorMJFPC} %{\marginpar{MJF+PC}}
	 {\hfill  (M.J. Feigenbaum and P. Cvitanovi\'c)}
\newcommand{\authorGV} %{\marginpar{GV+PC}}
	 {\hfill (G. Vattay)}
\newcommand{\authorGVGTPC} %{\marginpar{GV+PC}}
	 {\hfill (G. Vattay, G. Tanner and P. Cvitanovi\'c)}
\newcommand{\authorGVPC} %{\marginpar{GV+PC}}
	 {\hfill (G. Vattay and P. Cvitanovi\'c)}
\newcommand{\authorNW} %{\marginpar{FC}}
	 {\hfill (N. Whelan)}
\newcommand{\authorAW} %{\marginpar{FC}}
	 {\hfill (A. Wirzba)}
\newcommand{\authorCV} %{\marginpar{FC}}
	 {\hfill (P. Cvitanovi\'c and L.V. Vela-Arevalo)}
\newcommand{\authorCW} %{\marginpar{FC}}
	 {\hfill (P. Cvitanovi\'c and A. Wirzba)}
\newcommand{\authorWCW} %{\marginpar{FC}}
	 {\hfill (A. Wirzba, P. Cvitanovi\'c and N. Whelan)}


\newcommand{\file}[1]{$\footnotemark\footnotetext{{\bf file} #1}$}
%\newcommand{\lecture}{\addtocontents{toc}{\sf\small lecture: }}
\newcommand{\lecture}[2]{ \addtocontents{toc}
           {{\scriptsize #1}{\sf\small lecture: \scriptsize #2}} }


%%%%%%%%%%%%%%% REFERENCING EQUATIONS ETC. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\rf}     [1] {~\cite{#1}}
\newcommand{\refref} [1] {ref.~\cite{#1}}
\newcommand{\refRef} [1] {Ref.~\cite{#1}}
\newcommand{\refrefs}[1] {refs.~\cite{#1}}
\newcommand{\Refrefs}[1] {Refs.~\cite{#1}}
\newcommand{\refeq}  [1] {(\ref{#1})}
\newcommand{\refeqs} [2]{(\ref{#1}--\ref{#2})}
\newcommand{\refpage}[1] {page~\pageref{#1}}
\newcommand{\reffig} [1] {figure~\ref{#1}}
\newcommand{\reffigs} [2] {figures~\ref{#1} and~\ref{#2}}
\newcommand{\refFig} [1] {Figure~\ref{#1}}
\newcommand{\refFigs} [2] {Figures~\ref{#1} and~\ref{#2}}
\newcommand{\reftab} [1] {table~\ref{#1}}
\newcommand{\refTab} [1] {Table~\ref{#1}}
\newcommand{\reftabs}[2] {tables~\ref{#1} and~\ref{#2}}
\newcommand{\refsect}[1] {sect.~\ref{#1}}
\newcommand{\refsects}[2] {sects.~\ref{#1} and \ref{#2}}
\newcommand{\refSect}[1] {Sect.~\ref{#1}}
\newcommand{\refchap}[1] {chapter~\ref{#1}}
\newcommand{\refChap}[1] {Chapter~\ref{#1}}
\newcommand{\refchaps}[2] {chapters~\ref{#1} and \ref{#2}}
\newcommand{\refappe}[1] {appendix~\ref{#1}}
\newcommand{\refappes}[2] {appendices~\ref{#1} and \ref{#2}}
\newcommand{\refAppe}[1] {Appendix~\ref{#1}}
\newcommand{\refrem} [1] {remark~\ref{#1}}
\newcommand{\refexam}[1] {example~\ref{#1}}
\newcommand{\refexer}[1] {exercise~\ref{#1}}
\newcommand{\refsolu}[1] {solution~\ref{#1}}
\newcommand{\refExer}[1] {Exercise~\ref{#1}}
\newcommand{\exerbox}[1]{
         \marginpar[{%
           	\color{green} 
		\raisebox{-0.5ex}[1.0ex][1.0ex]{\huge \ding{46}}
	   	\sf ~\ref{#1}\\ \footnotesize page~\pageref{#1} 
                   }]% 
          {	\raggedright
           	\color{green} 
		\raisebox{-0.5ex}[1.0ex][1.0ex]{\huge \ding{46}}
	   	\sf ~\ref{#1}\\ \footnotesize page~\pageref{#1} 
          } 
                        }
           %\includegraphics[width=0.04\textwidth]{Fig/padPencil.eps}
           %\includegraphics[width=0.04\textwidth]{Fig/exercise.ps}
           %\includegraphics[width=0.04\textwidth]{Fig/archive.ps}

\newcommand{\advSect}{\marginpar{\fbox{\sf $\bullet$ advanced section $\bullet$ } } }
\newcommand{\toSect}[1]{\marginpar[{
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize \refsect{#1} }
				  }]{ 
          	\raggedright
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize \refsect{#1} }
                                  } }
\newcommand{\toChap}[1]{\marginpar[{
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize ~\refchap{#1} }
				  }]{ 
          	\raggedright
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize ~\refchap{#1} }
                                  } }
		%\includegraphics[width=0.6cm]{Fig/thisWay.ps}

\newcommand{\toAppe}[1]{\marginpar[{
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize \refappe{#1} }
				  }]{ 
          	\raggedright
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize \refappe{#1} } 
                                  } }
\newcommand{\toRem}[1]{\marginpar[{
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize \refrem{#1} }
				 }]{ 
          	\raggedright
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize \refrem{#1} }
                                  } }
\newcommand{\toExam}[1]{\marginpar[{
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize \refrem{#1} }
				 }]{ 
          	\raggedright
		\color{green} 
		\raisebox{-1.0ex}[1.0ex][1.0ex]{\huge \ding{43}}
		{\sf \footnotesize \refrem{#1} }
                                  } }
\newcommand{\tangent}{\includegraphics[width=0.08\textwidth]{Fig/chili.eps}~~}
%\newcommand{\tangent}{\marginpar{\fbox{ \includegraphics{Fig/chili.ps} } } }
\newcommand{\fastTrack}[1]
           {\hfill {\raisebox{-3.0ex}[4.5ex][3.5ex]{
                              \includegraphics[width=1.25cm]{Fig/thisWay.ps}
                                                   }
			\begin{minipage}[t]{0.25\textwidth}
			{\sf \footnotesize
			       fast track: \\
                               \refsect{#1}, p.~\pageref{#1}
                        } 
			\end{minipage}
                    }
           }
\newcommand{\fastTrackChap}[1]
           {\hfill {\raisebox{-3.0ex}[4.5ex][3.5ex]{
                              \includegraphics[width=1.25cm]{Fig/thisWay.ps}
                                                   }
			\begin{minipage}[t]{0.25\textwidth}
			{\sf \footnotesize
			       fast track: \\
                               \refchap{#1}, p.~\pageref{#1}
                        } 
			\end{minipage}
                    }
           }
\newcommand{\inDepth}[1]
           {\hfill {\raisebox{-3.0ex}[4.5ex][3.5ex]{
                         \includegraphics[width=1.24cm]{Fig/eyep.ps}
                                                   }
			\begin{minipage}[t]{0.25\textwidth}
			{\sf \footnotesize
			       in depth: \\
                               \refsect{#1}, p.~\pageref{#1}
                        } 
			\end{minipage}
                    }
           }
\newcommand{\inDepthChap}[1]
           {\hfill {\raisebox{-3.0ex}[4.5ex][3.5ex]{
                         \includegraphics[width=1.24cm]{Fig/eyep.ps}
                                                   }
			\begin{minipage}[t]{0.25\textwidth}
			{\sf \footnotesize
			       in depth: \\
                               \refchap{#1}, p.~\pageref{#1}
                        } 
			\end{minipage}
                    }
           }
\newcommand{\inDepthAppe}[1]
           {\hfill {\raisebox{-3.0ex}[4.5ex][3.5ex]{
                         \includegraphics[width=1.24cm]{Fig/eyep.ps}
                                                   }
			\begin{minipage}[t]{0.25\textwidth}
			{\sf \footnotesize
			       in depth: \\
                               \refappe{#1}, p.~\pageref{#1}
                        } 
			\end{minipage}
                    }
           }

%%%%%%%%%%%%%%% EQUATIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\beq}{\begin{equation}}
\newcommand{\continue}{\nonumber \\ }
\newcommand{\nnu}{\nonumber}
\newcommand{\eeq}{\end{equation}}
\newcommand{\ee}[1] {\label{#1} \end{equation}}
\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\ceq}{\nonumber \\ & & }
\newcommand{\eea}{\end{eqnarray}}
\newcommand{\barr}{\begin{array}}
\newcommand{\earr}{\end{array}}

%%%%%%%%%%%%%%% VECTORS, MATRICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\MatrixII}[4]{
   \pmatrix{ {#1}  &  {#2} \cr
             {#3}  &  {#4} \cr} }

\newcommand{\MatrixIII}[9]{
   \pmatrix{ {#1}  &  {#2} &  {#3} \cr
             {#4}  &  {#5} &  {#6} \cr
             {#7}  &  {#8} &  {#9} \cr} }

\newcommand{\transpVectorII}[2]{
   \pmatrix{ {#1}  &  {#2}  \cr} }

\newcommand{\VectorII}[2]{
   \pmatrix{ {#1} \cr
             {#2} \cr} }

\newcommand{\VectorIII}[3]{
   \pmatrix{ {#1} \cr
             {#2} \cr
             {#3} \cr} }

\newcommand{\combinatorial}[2]{ {#1 \choose #2}}

%%%%%%%%%%%%%%% NUMBERED ENVIRONMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% REPLACE {13.5cm} by \textwidth counter in these environments

\newtheorem{exerc}{\textsf{\textbf{Exercise}}}[chapter]
% \newtheorem{exerc}{}[chapter]
% \newtheorem{exerc}{{$\bullet$}}[chapter]
 \newcommand{\exercise}[2]{
        \vskip -13mm
         \noindent
         \begin{exerc}{
\renewcommand{\theenumi}{\alph{enumi}}
\renewcommand{\labelenumi}{\textbf{(\alph{enumi})\ }}
 	{\noindent\small
         ~~\textsf{\textbf{#1}} ~
           \slshape\sffamily{#2}  } % \textsl would not work...
	}
         \vskip -1mm 
% removed the line: % \noindent\rule[.1mm]{\linewidth}{.5mm}
         \end{exerc}
                          }

\newcommand{\Exercise}[2]{		%environment for obligatory problems
        \vskip -13mm
        \noindent
        \begin{exerc}{
\renewcommand{\theenumi}{\alph{enumi}}
\renewcommand{\labelenumi}
	{\textsf{\textbf{ (\alph{enumi})\ }}}
        {\noindent
         ~~\textsf{\textbf{\underline{#1}}} ~
           \slshape\sffamily{#2}  } % \textsl would not work...
        }
         \vskip -1mm
        \end{exerc}
                          }

% from LaTeX style file for the CUP standard designs 5a to 9b
% \newtheorem{exerc}{Exercise}[chapter]
% \newcommand{\exercise}[2]{
% %        \vskip -12mm
%          \begin{quotation}
%         \noindent\rule[.1mm]{10.7cm}{.2mm} 
% 	 % \vskip -22mm 
%          \noindent
%          \begin{exerc}{
%           \noindent ~~{\small\em\bf #1 ~}\small\em #2 }
%           \vskip -1mm \noindent\rule[.1mm]{10.7cm}{.5mm}
%  	\end{exerc}
%          \end{quotation}
%   			  }
 
\newcommand{\solution}[3]{
         \vskip -4mm
        {\noindent\small
         ~~\textsf{\textbf{  Solution \ref{#1}:   %NUMBER
			    ~#2}}		  %TITLE 
           \slshape\sffamily{#3}   		  %TEXT
         }
         \vskip  4mm 
% removed the line: % \noindent\rule[.1mm]{\linewidth}{.5mm}
                        }

\newtheorem{rmark}{{\small\textsf{\textbf{Remark}}}}[chapter]
\newcommand{\remark}[2]{
        \begin{quotation}
        \begin{rmark}
        {\small\em\noindent {\small\sf \underline{ #1} ~} #2 }
	\end{rmark}
	\end{quotation}
 			  }

\newtheorem{exmple}{\noindent\small\textsf{\textbf{Example}}}[chapter]
\newcommand{\example}[2]{
	\vskip -13mm
        \begin{offset}
        \begin{exmple}
           \noindent\small
           \textsf{\textbf{#1}} ~ 
	   \slshape\sffamily{#2}  
	   % \textsl would not work...
	\end{exmple}
	\end{offset}
        \vskip -1mm
 			 }

%%%% fine tuning floatingfigure \usepackage[nooneline] captions %%%%%
        \renewcommand{\captionfont}{\small \sffamily}
        \renewcommand{\captionlabelfont}{\small \bfseries \rmfamily}
        % \renewcommand{\captionlabeldelim}{.\quad}
        % \setlength{\captionmargin}{10pt}

%   \FIG{#1}	% \includegraphics[width=0.40\textwidth]{Fig/f_name.ps}
%	{#2}	% short caption text
%	{#3}	% full caption text
%	{#4}	% f-figure-label
% 		defined here:
\newcommand{\FIG}[4]{\begin{figure}
		      \hspace*{0.10\textwidth}%
		      \begin{minipage}[b]{1.00\textwidth}
		      \noindent{#1}
		      %\centering{#1}
                      \caption[#2]{#3}
                      \label{#4}
		      \end{minipage}
		      \end{figure} }

%% Eventually get rid of {floatingfigure}
%  \FFIG{#1}    % width=?cm, ... here
%       {#2}    % Fig/f_name.ps
%       {#3}    % short caption text
%       {#4}    % full caption text
%       {#5}    % f-figure-label
\newcommand{\FFIG}[5]{\begin{floatingfigure}[v]{0.40\textwidth}
                      \noindent
                      \includegraphics[#1]{#2}
                      \caption[#3]{#4}
                      \label{#5}
		      \end{floatingfigure} }

%   \BFIG{#1}	% width=#1\textwidth
%        {#2}	% f_name.ps
%	 {#3}	% short caption text
%	 {#4}	% full caption text
%	 {#5}	% f-figure-label
% 		defined here:
\newcommand{\BFIG}[5]{\begin{figure}
		      \hspace*{0.10\textwidth}%
		      \begin{minipage}[b]{1.00\textwidth}
		      \centering{
                      \includegraphics[width=#1\textwidth]{Fig/#2}
			         }
                      \caption[#3]{#4}
                      \label{#5}
		      \end{minipage}
		      \end{figure} }

%  \SFIG{#1}    % f_name.eps
%       {#2}    % short caption text
%       {#3}    % full caption text
%       {#4}    % f-figure-label
\newcommand{\SFIG}[4]{\begin{figure}
		      %\hspace*{-0.10\textwidth}
		      \hspace*{0.10\textwidth}
		      \begin{minipage}[b]{0.55\textwidth}
                      \caption[#2]{#3}
                      \label{#4} 
		      \end{minipage}~~~~~%
		      \begin{minipage}[b]{0.40\textwidth}
                      \includegraphics[width=1.00\textwidth]{Fig/#1}
		      \end{minipage}
		      %\hfill
		      \end{figure} }

%%%%%%%%%%%%%%  Abbreviations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\etc}{{\em etc.}}		% etcetera in italics
\newcommand{\ie}{{that is}}		% use Latin or English?  Decide later.
\newcommand{\cf}{{\em cf.}}
					% keep homepage flexible:
\newcommand{\wwwcb}{{\tt www.nbi.dk/ChaosBook}}
\newcommand{\wwwQFT}{{\tt www.nbi.dk/FieldTheory}}
\newcommand{\wwwcnsQFT}{{\tt www.cns.physics.gatech.edu/FieldTheory}}

%%%%%%%%%%%%%%% Evolution operators, zetas %%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\evOper}{evolution oper\-ator}
\newcommand{\EvOper}{Evolution oper\-ator}
 %% \newcommand{\evOp}{Ruelle operator} %could be ``evolution'' instead?
%\newcommand{\FPoper}{Frobenius-Perron oper\-ator}
\newcommand{\FPoper}{Perron-Frobenius oper\-ator} % Pesin's ordering
\newcommand{\FP}{Perron-Frobenius}
\newcommand{\maslov}{topological}
\newcommand{\Maslov}{Topological}
%\newcommand{\Maslov}{Keller-Maslov}
\newcommand{\jacobian}{Jacobian}		% determinant
\newcommand{\jacobianM}{Jacobian matrix}	% matrix
\newcommand{\jacobianMs}{Jacobian matrices}	% matrices
\newcommand{\dzeta}{dyn\-am\-ic\-al zeta func\-tion}
\newcommand{\Dzeta}{Dyn\-am\-ic\-al zeta func\-tion}
\newcommand{\tzeta}{top\-o\-lo\-gi\-cal zeta func\-tion}
\newcommand{\Tzeta}{Top\-o\-lo\-gi\-cal zeta func\-tion}
\newcommand{\BERzeta}{BER zeta func\-tion}
%\newcommand{\tzeta}{Artin-Mazur zeta func\-tion} %alternative to topological
\newcommand{\qS}{semi\-classical zeta func\-tion}
%\newcommand{\qS}{Gutz\-willer-Voros zeta func\-tion}
\newcommand{\Gt}{Gutz\-willer trace formula}
\newcommand{\Fd}{spec\-tral det\-er\-min\-ant}
\newcommand{\fd}{spec\-tral det\-er\-min\-ant}
\newcommand{\FD}{Spec\-tral det\-er\-min\-ant}
\newcommand{\cFd}{semiclass\-ic\-al spec\-tral det\-er\-mi\-nant}
\newcommand{\cFD}{Semiclass\-ic\-al spec\-tral det\-er\-mi\-nant}
% \newcommand{\cFd}{semiclass\-ic\-al Fred\-holm det\-er\-mi\-nant}
\newcommand{\Vd}{Vattay det\-er\-mi\-nant}
\newcommand{\cycForm}{cycle averaging formula}
\newcommand{\CycForm}{Cycle averaging formula}
\newcommand{\freeFlight}{mean free flight time}
\newcommand{\FreeFlight}{Mean free flight time}
\newcommand{\pdes}{partial differential equations}
\newcommand{\Pdes}{Partial differential equations}

%%%%%%%%%%%%%%% Sundry symbols within math eviron.: %%%%%%%%%%%%

\newcommand{\obser}{a}		% an observable from phase space to R^n
\newcommand{\Obser}{A}		% time integral of an observable
\newcommand{\onefun}{\iota}	% the function that returns one no matter what
\newcommand{\defeq}{=}		% the different equal for a definition
\newcommand {\deff}{\stackrel{\rm def}{=}}
\newcommand{\reals}{\mathbb{R}}
\newcommand{\complex}{\mathbb{C}}
\newcommand{\integers}{\mathbb{Z}}
\newcommand{\rationals}{\mathbb{Q}}
\newcommand{\naturals}{\mathbb{N}}
\newcommand{\LieD}{{{\cal L}\!\!\llap{-}\,\,}}  % {{\pound}} % Lie Derivative 
\newcommand{\half}{{\scriptstyle{1\over2}}}
\newcommand{\pde}{\partial}
\renewcommand\Im{{\rm Im\,}}
\renewcommand\Re{{\rm Re\,}}
\renewcommand{\det}{\mbox{\rm det}\,}
\newcommand{\Det}{\mbox{\rm Det}\,}
\newcommand{\tr}{\mbox{\rm tr}\,}
\newcommand{\Tr}{\mbox{\rm tr}\,}
%\newcommand{\Tr}{\mbox{Tr}\,}
\newcommand{\sign}[1]{\sigma_{#1}}
%\newcommand{\sign}[1]{{\rm sign}(#1)}
\newcommand{\DiffC}{D}		% diffusion constant
\newcommand{\mInv}{{I}}			        % material invariant 
\newcommand{\msr}{{\rho}}		        % measure 
\newcommand{\Msr}{{\mu}}		        % coarse measure 
\newcommand{\dMsr}{{d\mu}}		        % measure infinitesimal
\newcommand{\SRB}{{\rho_0}}		        % natural measure 
\newcommand{\vol}{{V}}		        	% volume of i-th tile
\newcommand{\prpgtr}[1]{\delta\negthinspace\left( {#1} \right)}
%\newcommand{\Zqm}{Z_{qm}}			% Gutz-Voros zeta function
\newcommand{\Zqm}{{\det(\hat{H} - E)_{sc} }}	% semicls spectr. det:
\newcommand{\Fqm}{F_{qm}}
\newcommand{\zfct}[1]{\zeta ^{-1}_{#1}}     
\newcommand{\zetaInv}{{1/\zeta}}
% \newcommand{\zetaInv}{{\zeta^{-1}}}
\newcommand{\zetatop}{1/\zeta_{\mbox{\footnotesize top}}}
\newcommand{\zetaInvBER}[1]{1/\zeta_{\mbox{\footnotesize BER}}(#1)}
\newcommand{\BER}[1]{{\mbox{\footnotesize BER}}} % Baladi-Ruelle-Eckmann
\newcommand{\eigCond}{F}			% eigenvalue cond. function
\newcommand{\expct}    [1]{\left\langle {#1} \right\rangle}
\newcommand{\spaceAver}[1]{\left\langle {#1} \right\rangle}
\newcommand{\timeAver} [1]{\overline{#1}}
\newcommand{\pS}{{\cal M}}			% symbol for phase space 
\newcommand{\NWS}{\Omega}	   % symbol for the non--wandering set
\newcommand{\AdmItnr}{\Sigma}	   % set of admissible itineraries
\newcommand{\intM}[1]{{\int_\pS{\!d #1}\:}}	%phasespace integral
\newcommand{\Cint}[1]{\oint\frac{d#1}{2 \pi i}\;} %Cauchy contour integral
\newcommand{\PoincS}{{\cal P}}                  % symbol for Poincare section
\newcommand{\PoincM}{{P}}			% symbol for Poincare map
\newcommand{\arc}{{s}}		   % symbol for billiard wall arc
\newcommand{\mompar}{{p}}	   % symbol for billiard wall parall. momentum
%\newcommand{\PoincS}{\partial{\cal M}}          % billiard Poincare section
\newcommand{\Lop}{{\cal L}}	   % evolution operator
\newcommand{\Uop}{{\cal K}}	   % Koopman operator, Driebe notation
\newcommand{\Aop}{{\cal A}}	   % evolution generator
\newcommand{\Top}{{\cal T}}	   % transfer operator, like in statmech
\newcommand{\matId}{{\bf 1}}	   % matrix identity
\newcommand{\Mvar}{{A}}	   	   % matrix of variations
\newcommand{\jMps}{{\bf J}}	   % jacobiam matrix, full phase space
\newcommand{\jMConfig}{{\bf j}}	   % jacobiam matrix, configuration space
\newcommand{\jConfig}{j}	   % jacobian, configuration space
\newcommand{\monodromy}{{\bf J}}   % monodromy matrix, full Poincare cut
				   % Fredholm det jacobian weight:
\newcommand{\oneMinJ}[1]
           {\left|\det\!\left(\matId-\monodromy_p^{#1}\right)\right|}
\newcommand{\maslovInd}{{m}}  	   % Maslov index
\newcommand{\ExpaEig}{\Lambda}	   
\newcommand{\eigenvL}{{s}}	   
\newcommand{\inFix}[1]{{\in \mbox{\footnotesize Fix}f^{#1}}}
\newcommand{\inZero}[1]{{\in \mbox{\footnotesize Zero} \, f^{#1} }}
\newcommand{\xzero}[1]{{x_{#1}^{*}}}
\newcommand{\fractal}{{\cal F}}
\newcommand{\contract}{F}
\newcommand{\presentation}{P}

     %%%%%%%%%% flows: %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\flow[2]{{f^{#1}(#2)}}
\newcommand\invFlow{F}
\newcommand\hflow[2]{{\hat{f}^{#1}(#2)}}
\newcommand\timeflow{{f^t}}
\newcommand\tflow[2]{{\tilde{f}^{#1}(#2)}}
%\newcommand\tflow{\tilde{f}^\tau}	      %RECHECK USE OF THIS!
\newcommand\xInit{{x_0}}		%initial x
%\newcommand\xInit{\xi}		%initial x, Spiegel notation
\newcommand\pSpace{x}		% phase space x=(q,p) coordinate
\newcommand\coord{q}		% configuration space p coordinate
\newcommand{\para}{\parallel}
\newcommand\stagn{q}		%equilibrium/stagnation point suffix
\newcommand\multiX{x}		%multi point n-dim vector
\newcommand\multiF{f}		%multi point n-dim vector mapping

     %%%%%%%%%% periods: %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\period[1]{{T_{#1}}}			%continuous cycle period
%\newcommand\period[1]{{\tau_{#1}}}
\newcommand{\cl}[1]{{n_{#1}}}	% discrete length of a cycle, Predrag
%\newcommand{\cl}[1]{|#1|}	% the length of a periodic orbit, Ronnie
\newcommand{\nCutoff}{N}	% maximal cycle length
				% maximal stability cutoff:
\newcommand{\stabCutoff}{\ExpaEig_{\mbox{\footnotesize max}}}
\newcommand{\timeSegm}[1]{{\tau_{#1}}}		%billiard segment time period
\newcommand{\timeStep}{{\delta \tau}}		%integration step
\newcommand{\deltaX}{{\delta x}}		%trajectory displacement
\newcommand{\unitVec}{\hat{n}}		%unit vector
\newcommand\Lyap{\lambda}			%Lyapunov exponent
\newcommand\LyapTime{T_{\mbox{\footnotesize Lyap}}}	%Lyapunov time
\newcommand{\hatx}{{\hat{x}}}
% \newcommand{\hatx}{{\hat{x}_t}}               %RECHECK USE OF THIS!
\newcommand{\hatp}{{\hat{x}_p}}
\newcommand{\phat}{{\hat{p}}}
\newcommand{\curvR}{\rho}			%billiard curvature
\newcommand{\dz}{{\delta z}}
\newcommand{\dth}{{\delta \theta}}
\newcommand{\delh}{{\delta h}}
\newcommand{\PP}{{\cal P}}
\newcommand{\NN}{{\cal N}}

%%%%%%%%%%%%%%% symbolic dynamics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\MarkGraph}{Markov graph}
\newcommand{\admissible}{admissible}
\newcommand{\inadmissible}{inadmissible}
\newcommand{\cycle}[1]{{$\overline{#1}$}}
\newcommand{\cycpt}{_{p,m}}
\newcommand\sumprime{\mathop{{\sum}'}}
\newcommand{\pseudos}{\pi}
% \newcommand{\pseudos}{{p_1+p_2+\dots+p_k}}
% \newcommand{\pseudos}{{\{p_1 p_2 \dots p_k\}}}
\newcommand{\block}[1]{#1}
\newcommand{\prune}[1]{\_{#1}\_}        % fits into math env.
%\newcommand{\prune}[1]{\ldots{#1}\ldots}
\newcommand{\strng}[1]{$\_#1\_$}	% fits into text without $'s
\newcommand{\biinf}[2]{\cdots#1.#2\cdots}
\newcommand{\rctngl}[2]{[#1.#2]}
\newcommand{\BKsym}[1]{S_{#1}}
\newcommand{\Ksym}[1]{\sigma_{#1}}
\newcommand{\Ssym}[1]{{s_{#1}}}
\newcommand{\gmax}{\hat{\gamma}}
\newcommand{\Spast}{S^\textrm{-}}		% past itenerary
\newcommand{\Sfuture}{S^\textrm{\scriptsize +}}	% future itenerary
\newcommand{\Sbiinf}{S}				% biinf. itenerary
\newcommand{\str}{\epsilon_{1},\epsilon_{2}, \ldots } % Ronnie's problems

%%%%%%%%%%%%%%% Ronnie's problems %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\estr}[1] {\epsilon_{1},\epsilon_{2}, \ldots, \epsilon_{#1}}
\newcommand{\eestr}[2] {#1,\epsilon_{1},\epsilon_{2}, \ldots,\epsilon_{#2}}

%%%%%%%%%%%%%% diag.tex specific %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\Lmat}[1]{{{\bf L}_{#1}}}      % evolution matrix

%%%%%%%%%%%% loopDef.tex, defCrete.tex specific %%%%%%%%%%%%%
% Predrag	defCrete.tex			 4mar2003
% Predrag	loopDefs.tex			10jul2003

\newcommand{\descent}{Newton descent}
\newcommand{\Descent}{Newton Descent}
\newcommand{\costFct}{cost function}	% functional to minimize
\newcommand{\costF}{F^2}  		% cost function, 
\newcommand{\Loop}{L}
\newcommand{\pVeloc}{v}			% phse-space velocity 
\newcommand{\lSpace}{\tilde{x}}		% a point on a loop 
\newcommand{\lVeloc}{\tilde{v}}		% loop tangent
\newcommand{\damp}{\Delta\tau}		% descrete fititous time step
% \newcommand{\pSpaceDer}[1]{x^{(#1)}}
% \newcommand{\lSpaceDer}[1]{\tilde{x}^{(#1)}}

%%%%%%%%%%%% END loopDef.tex, defCrete.tex specific %%%%%%%%%

%%%%%%%%%%%%%%% Lorentz gas section %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\hn{\hat n}
\newcommand\hM{\hat \pS}
%\def\hM{\widehat M}
\newcommand\hx{\hat x}
\def\tx{\tilde x}
\def\tpk{_{\tilde p,k}}
\def\tpk{}              %why redefined?
\def\ttime{\sigma_{\tilde{p}}}

%%%%%%%%%%%%%%% Henon map section %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\logisticm}{quadratic map}
\newcommand{\Logisticm}{Quadratic map}
\newcommand{\stretchf}{``stretch \&\ fold''}
\newcommand{\Stretchf}{``Stretch \&\ fold''}
\newcommand{\ofm}{once-folding map}
\newcommand{\Ofm}{Once-folding map}
\newcommand{\mHt}{map of the H\'enon type}
\newcommand{\mHts}{maps of the H\'enon type}
\newcommand{\MHts}{Maps of the H\'enon type}
\newcommand{\opres}{orientation preserving}
\newcommand{\Opres}{Orientation preserving}
\newcommand{\orev}{orientation reversing}
\newcommand{\Orev}{Orientation reversing}
\newcommand{\nws}{non--wandering set}
\newcommand{\stranges}{non--wandering set}
%\newcommand{\stranges}{strange set}
\newcommand{\ki}{kneading value}
\newcommand{\Ki}{Kneading value}
\newcommand{\ks}{kneading sequence}
\newcommand{\turn}{turning point}    % {turnback} ??
\newcommand{\pturn}{primary turning point}    % {turnback} ??
\newcommand{\Pturn}{Primary turning point}    % {Turnback} ??
\newcommand{\topc}{topological coordinate}
\newcommand{\Topc}{Topological coordinate}
\newcommand{\critVal}{f(x_c)}
\newcommand{\topcv}{maximal value}
\newcommand{\Topcv}{Maximal value}
\newcommand{\toppar}{topological parameter}
\newcommand{\toppp}{topological parameter plane}
\newcommand{\topp}{symbol square}
\newcommand{\Topp}{Symbol square}
\newcommand{\bimappr}{bimodal approximation}
\newcommand{\Bimappr}{Bimodal approximation}
\newcommand{\henappr}{bimodal approximation}
\newcommand{\fourfa}{four-folds approximation}
\newcommand{\Fourfa}{Four-folds approximation}
\newcommand{\snbif}{saddle-node bifurcation}
\newcommand{\Snbif}{Saddle-node bifurcation}

%%%%%%%%%%%%%%% symmetric, asymmetric orbits: %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\sym}{{s}}
\newcommand{\nsym}{{n_s}}
\newcommand{\asym}{{a}}
\newcommand{\nasym}{{n_a}}
% fundamental domain:
\newcommand{\pf}{{\tilde p}}
\newcommand{\nf}{n_{\tilde p}}
\newcommand{\symf}{{\tilde s}}
\newcommand{\nsymf}{n_{\tilde s}}

%%%%%%%%%%%%%% Quantum mechanical stuff %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\HamPrincFct}[4]{R_{#4}({#1},{#2},{#3})}
			   % \HamPrincFct{q}{q'}{t}{j}

%%%%%%%%%%%%%% SPECIFIC TO lattFT.tex NOTES %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\unit}{{\bf 1}}
\newcommand{\hopMat}{{\bf h}}
\newcommand{\hop}{h}
\newcommand{\fix}{\marginpar{$\diamond$}}
\newcommand{\source}{{J}}
\newcommand{\sourceFT}{{\tilde{J}}}
\newcommand{\derSource}{{d~\over d\source}}
\newcommand{\derSourceFT}{{d~\over d\sourceFT}}
%\newcommand{\field}{{\phi}}		% modified in lattFT.tex 
\newcommand{\field}{{x}}
\newcommand{\fieldFT}{{\tilde{\phi}}}
\newcommand{\derField}{{d~\over d\field}}
\newcommand{\saddleField}{{\field^c}}
\newcommand{\saddleCoord}{{\coord^c}}
\newcommand{\Laplacian}{\Delta}
% \newcommand{\Prpgtr}{{G_0}}		% modified in lattFT.tex 
\newcommand{\Prpgtr}{{M}}
\newcommand{\PrpgtrFT}{{\tilde{G}_0}}
% \newcommand{\InvPrpgtr}{{G_0^{-1}}}	% modified in lattFT.tex
\newcommand{\InvPrpgtr}{{M^{-1}}}
\newcommand{\GreenF}{{G}}
\newcommand{\Df}[1]{f^{'}_{#1}}
\newcommand{\nosum}{\not\!\!{\scriptstyle\sum}}
% \newcommand{\etal}{{\em et al.}}		% etcetera in italics
\newcommand{\doublespace}{\baselineskip = \normalbaselineskip \multiply\baselineskip by 2}
%%%%%%%%%%%%%% end of SPECIFIC TO lattFT.tex NOTES %%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%  gli commandi di Commandottore Roberto   %%%%%%%%%%%%

\newcommand {\tidue}{{\mbox{\bf T}}^{2}}
\newcommand {\bom}[1]{\mbox{\boldmath $#1$}}
\newcommand {\polit}{{\cal P}_{T}}
\newcommand {\id}{{\ \hbox{{\rm 1}\kern-.6em\hbox{\rm 1}}}}
\newcommand {\ep}{\epsilon}

%%%%%%% Wirzba scattering.tex  %%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\gesim}{\mbox{\raisebox{-.6ex}{$\,{\stackrel{>}{\sim}}\,$}}}
\newcommand{\lesim}{\mbox{\raisebox{-.6ex}{$\,{\stackrel{<}{\sim}}\,$}}}
\newcommand{\Ageom}[1]{{\bf A}^{#1}}
\newcommand{\Aghost}[1]{{\underline{\bf A}}^{#1}}
\newcommand{\Acreep}[1]{{\mathbb{A}}^{#1}}
%\newcommand{\Acreep}[1]{{\hat{\bf A}}^{#1}}

%%%%%%%%%%%%%%%%%%%%%% birdtracks SPECIFIC %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\btrack}[1]{\raisebox{-2.0ex}[3.5ex][2.5ex]
	{\includegraphics[height=5ex]{figs/f_#1.eps}\negthinspace} }
   	%{\epsfig{file=figs/f_#1.eps,height=5ex}\negthinspace} }
%% A is 7/5-ths taller
\newcommand{\btrackA}[1]{\raisebox{-3.0ex}[4.5ex][3.5ex]
         { \epsfig{file=figs/f_#1.eps,height=7ex}\negthinspace} }
%% B is 9/5-ths taller
\newcommand{\btrackB}[1]{\raisebox{-4.0ex}[5.5ex][4.5ex]
          { \epsfig{file=figs/f_#1.eps,height=9ex}\negthinspace} }
%% BB is 11/5 larger
\newcommand{\btrackBB}[1]{\raisebox{-5.0ex}[6.5ex][5.5ex]
          { \epsfig{file=figs/f_#1.eps,height=11ex}\negthinspace} } 
%% C is 1/2 smaller
\newcommand{\btrackC}[1]{\raisebox{-0.4ex}[1.75ex][1.25ex]
          { \epsfig{file=figs/f_#1.eps,height=2.5ex}\negthinspace} }
%% birtrack to be drawn:
\newcommand{\zzzz}{{\tt birdTrack}}

%%%%%%%%%%%%%%%%%% FEYNMANN DIAGRAMS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\thicklines
\newlength{\Fsize}   % allow for easy resizing of diagrams
\newlength{\Fdotsize}
\setlength{\Fsize}{20pt}
\setlength{\Fdotsize}{5pt}
\setlength{\unitlength}{\Fsize}
\newcommand{\Fdot}{  % vertex
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fdotsize}
	\put(0,0){\circle*{1}}
        \end{picture}}
%Propagator naming conventions: \F(d|D)(h|[c](u|d|l|r)(u|d|l|r))
%d=dotted, D=solid, h=horizontal, c=curved, u=up, d=down, l=left, r=right
%The straight propagators are specified u|d then l|r
%The curved propagators end up in the location specified by the last letter
\newcommand{\Fdh}{   % horizontal dotted propagator
	\begin{picture}(0,0)
	\setlength{\unitlength}{\Fsize}
	\qbezier[10](0,0)(0.5,0)(1,0)
	\end{picture}}
\newcommand{\FDh}{   % horizontal solid propagator
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
	\put(0,0){\line(1,0){1}}
        \end{picture}}
\newcommand{\FDur}{  % diagonal solid propagators
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
	\put(0,0){\line(1,1){0.7}}
        \end{picture}}
\newcommand{\FDdr}{ 
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \put(0,0){\line(1,-1){0.7}}
        \end{picture}}
\newcommand{\FDul}{  
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \put(0,0){\line(-1,1){0.7}}
        \end{picture}}
\newcommand{\FDdl}{
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \put(0,0){\line(-1,-1){0.7}}
        \end{picture}}
\newcommand{\Fdcul}{  % curved propagators
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
	\qbezier[15](0,0)(-1,1)(-1,0)
        \end{picture}}
\newcommand{\FDcdl}{  
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \qbezier(0,0)(-1,-1)(-1,0)
        \end{picture}}
\newcommand{\Fdcur}{
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \qbezier[15](0,0)(1,1)(1,0)
        \end{picture}}
\newcommand{\FDcur}{
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \qbezier(0,0)(1,1)(1,0)
        \end{picture}}
\newcommand{\FDcdr}{
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \qbezier(0,0)(1,-1)(1,0)
        \end{picture}}
\newcommand{\Fdclu}{
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \qbezier[20](0,0)(-1,1)(1,1)
        \end{picture}}
\newcommand{\FDcld}{
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \qbezier(0,0)(-1,-1)(1,-1)
        \end{picture}}
\newcommand{\FDcru}{
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \qbezier(0,0)(1,1)(-1,1)
        \end{picture}}
\newcommand{\FDcrd}{
        \begin{picture}(0,0)
        \setlength{\unitlength}{\Fsize}
        \qbezier(0,0)(1,-1)(-1,-1)
        \end{picture}}
\setlength{\unitlength}{1pt}


%%%%%%%%%%%%%%  Bibliography abbreviations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\newcommand{\AP}[1]{{\em Ann.\ Phys.}\/ {\bf #1}}
%\newcommand{\CHAOS}[1]{{\em CHAOS}\/ {\bf #1}}
%\newcommand{\CM}[1]{{\em Cont.\ Math.}\/ {\bf #1}}
%\newcommand{\CMP}[1]{{\em Commun.\ Math.\ Phys.}\/ {\bf #1}}
%\newcommand{\INCB}[1]{{\em Il Nuov.\ Cim.\ B}\/ {\bf #1}}
%\newcommand{\JCP}[1]{{\em J.\ Chem.\ Phys.}\/ {\bf #1}}
%\newcommand{\JETP}[1]{{\em Sov.\ Phys.\ JETP}\/ {\bf #1}}
%\newcommand{\JETPL}[1]{{\em JETP Lett.}\/ {\bf #1}}
%\newcommand{\JMP}[1]{{\em J.\ Math.\ Phys.}\/ {\bf #1}}
%\newcommand{\JMPA}[1]{{\em J.\ Math.\ Pure Appl.}\/ {\bf #1}}
%\newcommand{\JPA}[1]{{\em J.\ Phys.}\/ {\bf A  #1}}
%\newcommand{\JPB}[1]{{\em J.\ Phys.}\/ {\bf B  #1}}
%\newcommand{\JPC}[1]{{\em J.\ Phys.\ Chem.}\/ {\bf #1}}
%\newcommand{\JchemP}[1]{{\em J.\ Chem.\ Phys.}\/ {\bf #1}}
%\newcommand{\NPA}[1]{{\em Nucl.\ Phys.}\/ {\bf A #1}}
%\newcommand{\NPB}[1]{{\em Nucl.\ Phys.}\/ {\bf B #1}}
%\newcommand{\NONLIN}[1]{{\em Nonlinearity}\/ {\bf #1}}
%\newcommand{\PLA}[1]{{\em Phys.\ Lett.}\/ {\bf A #1}}
%\newcommand{\PLB}[1]{{\em Phys.\ Lett.}\/ {\bf B #1}}
%\newcommand{\PRA}[1]{{\em Phys.\ Rev.}\/ {\bf A #1}}
%\newcommand{\PRD}[1]{{\em Phys.\ Rev.}\/ {\bf D #1}}
%\newcommand{\PRL}[1]{{\em Phys.\ Rev.\ Lett.}\/ {\bf #1}}
%\newcommand{\PST}[1]{{\em Phys.\ Scripta}\/ {\bf T #1}}
%\newcommand{\RMS}[1]{{\em Russ.\ Math.\ Surv.}\/ {\bf #1}}
%\newcommand{\USSR}[1]{{\em Math.\ USSR.\ Sb.}\/ {\bf #1}}
%\newcommand{\ZNat}[1]{{\em Z. Naturforschung}\/ {\bf #1}}

%%%%%%%%%%%%      stuff below this line will probably be dropped%%%%%%%%%%%

\renewcommand{\b}{\beta}
\newcommand{\w}{\omega}
\newcommand{\p}{2\pi}
\newcommand{\J}{\mbox{  \rule[.03ex]{.03em}{1.5ex} \hspace*{-0.9em} \rm J}}
\newcommand{\f}{\varphi}

% \newcommand{\R}{\mbox{  \rule[.07ex]{.03em}{1.5ex} \hspace*{-0.75em} \rm R}}
% \newcommand{\nextchapter}{\newpage{\pagestyle{empty}\cleardoublepage}}

%\newcommand {\vett}[2]{\bepar{c} #1 \\ #2 \epar}
%\newcommand {\vettc}[2]{\bepar{c,c} #1 & #2 \epar}
%\newcommand {\vettq}[2]{\left[ \begin{array}{c,c} #1 & #2 \end{array} \right]}
%\newcommand {\ron}{\rho_{n}}
%\newcommand {\ronu}{\rho_{n+1}}
%\newcommand {\ggat}{\Gamma_{T}}
%\newcommand {\gga}{\Gamma}
%\newcommand {\ggan}{\Gamma_{n}}
%\newcommand {\figurino}[3]{\begin{figure}[b]  \vspace{#1}
%            \caption{\protect\small #2}  \label{#3} \end{figure}}
% \newcommand {\zitadef}{\prod_{p}(1-t_{p})}
%\def\t{\tilde}
%\def\h{\hat}
%\def\tf{\tilde f}
%\def\hf{\hat f}
% \def\time{\sigma_p}
%		%% try to understand what does this do?:
% \def\pmb#1{\setbox0=\hbox{$#1$}\kern-.025em\copy0\kern-\wd0
%	     \kern-0.05em\copy0\kern-\wd0\kern-.025em\raise.0233em\box0}

	% Roberto's versions:
% \newcommand{\reals}{\mbox{\bf R}} % used in Ronnie's problems
% \newcommand {\natur}{{\hbox{{\rm I}\kern-.2em\hbox{\rm N}}}}
%\newcommand {\relativi}{{\ \hbox{{\rm Z}\kern-.4em\hbox{\rm Z}}}}
% \newcommand {\reali}{{\hbox{{\rm I}\kern-.2em\hbox{\rm R}}}}
% \newcommand{\RR}{{I\negthinspace\!R}}		% Reals: we honor Tresser

%%%% all \Fig to be eliminated in favor of \FIG eventually %%%%%%%%%
%%%% eventually eliminate epsfig by \includegraphics everywhere %%%%
%   \Fig{#1}	% \epsfig{file=figs/f_name.ps,width=?cm} ... here
%	{#2}	% short caption text
%	{#3}	% full caption text
%	{#4}	% f-figure-label
% 		defined here:
% \newcommand{\Fig}[4]{\begin{figure}
% 			\centering{#1}
%                       \caption[#2]{#3}
%                       \label{#4} \end{figure} }

%%%%%%%%%%%%%%%%%chapter bibliography%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% from LaTeX style file for the CUP standard designs 5a to 9b
% Copyright 1993 Cambridge University Press
% \def\thereferences#1{\section*{References}\bibliographylist}
% \let\endthereferences=\endlist
% \def\bibliographylist{%
%  \small\raggedright
%  \list{}{\labelwidth\z@
%   \leftmargin 2em% \advance\leftmargin\labelsep
%   \itemsep \z@ plus .1pt
%   \itemindent-\leftmargin}
%  \parindent\z@
%  \parskip\z@ plus .1pt\relax
%  \def\newblock{\hskip .11em plus .33em minus .07em}
%  \sloppy\clubpenalty4000\widowpenalty4000
%  \sfcode`\.=1000\relax
% }
% \let\endbibliographylist=\endlist
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% changes bars package collides with everything, abandoned Apr 2000
% \setlength{\changebarwidth}{0.5cm}	% margin changes bars width
% %?\setcounter{\changebargray}{85} 	% margin changes bars blackness
% \newcommand{\Preliminary}[1]{\cbstart #1 \cbend}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Joachim Mathiesen uses in
% \textbf{Term paper for the course Fysik711B fall semester 1999}
% \usepackage[british]{babel}   %PC: why?
% \usepackage{wrapfig}          %PC: why?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
