%  defHK.tex
%% last edit   			Predrag	 17 oct 1999
%%            			Predrag	 20 mar 1999
%% created   			Predrag  26 oct 1998

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% define abreviations used throughout the text 
%% to make it easier to change conventions
%% and also define Feynmann diagrams
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%% PAGE LAYOUT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






%\renewcommand{\arraystretch}{0.9}

%%%%%%%%%%%%%% SPECIFIC TO hk.tex ARTICLE %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\Lnoise}[1]{{\mathcal L}_{#1}}   % noisy evolution operator 
\newcommand{\Lmat}[1]{{{\bf L}_{#1}}}	   % evolution matrix
\newcommand{\Bmat}[1]{{{\bf B}_{#1}}}	   % perturbative evolution matrix
\newcommand{\Prpgtr}[1]{\Delta_{#1}}
\newcommand{\InvPrpgtr}[1]{\Delta^{-1}_{#1}}
\newcommand{\CrlMat}[1]{C_{#1}}
\newcommand{\InvCrlMat}[1]{C^{-1}_{#1}}
\newcommand{\field}{\phi}
\newcommand{\Df}[1]{f^{'}_{#1}}
\newcommand{\Shift}{S}
\newcommand{\mod}[1]{#1}
% \newcommand{\mod}[1]{\dot{#1}} % Dettmann's calculation
\newcommand{\const}[1]{\hat{#1}}
\newcommand{\nosum}{\not\!\!{\scriptstyle\sum}}
% \newcommand{\etal}{{\em et al.}}		% etcetera in italics

%%%%%%%%%%%%%%%%%%%%%% COMMENTS IN THE TEXT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% also search the text for lines starting with %%  to
%% locate various internal comments, recent edits etc.
%\newcommand{\PC}[1]{\marginpar{
%		\renewcommand{\baselinestretch}{0.7}
%		\footnotesize #1}
%		\renewcommand{\baselinestretch}{1.0}
%				}
\newcommand{\PC}[1]{$\footnotemark\footnotetext{PC: #1}$}
\newcommand{\CD}[1]{$\footnotemark\footnotetext{CD: #1}$}
\newcommand{\RM}[1]{\marginpar{\footnotesize RM: #1}}
\newcommand{\GV}[1]{$\footnotemark\footnotetext{GV: #1}$}
\newcommand{\GP}[1]{$\footnotemark\footnotetext{GP: #1}$}
\newcommand{\NS}[1]{$\footnotemark\footnotetext{NS: #1}$}

\newcommand{\file}[1]{$\footnotemark\footnotetext{{\bf file} #1}$}

%%%%%%%%%%%%%%% REFERENCING EQUATIONS ETC. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\rf}     [1] {~\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{\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{\refappe}[1] {appendix~\ref{#1}}
\newcommand{\refappes}[2] {appendices~\ref{#1}--\ref{#2}}
\newcommand{\refAppe}[1] {Appendix~\ref{#1}}

%%%%%%%%%%%%%%% 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}}

%% birdtracks:
\newcommand{\btrack}[1]{\raisebox{-2.0ex}[3.5ex][2.5ex]
        {\includegraphics[height=5ex]{#1.eps}\negthinspace} }
\newcommand{\btrackA}[1]{\raisebox{-3.0ex}[4.5ex][3.5ex]
         {\includegraphics[height=7ex]{#1.eps}\negthinspace} }
\newcommand{\btrackB}[1]{\raisebox{-4.0ex}[5.5ex][4.5ex]
          {\includegraphics[height=9ex]{#1.eps}\negthinspace} }

\newlength{\Fsize}   % allow for easy resizing of diagrams
\setlength{\Fsize}{20pt}

%

%%%%%%%%%%%%%%% NUMBERED ENVIRONMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \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}
                      % \noindent{#1}
                      % \centering{#1}
                      {#1}
                      \caption[#2]{#3}
                      \label{#4} \end{figure} }

%%%%%%%%%%%%%%  Abbreviations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\etc}{{\em etc}}		% etcetera in italics
\newcommand{\ie}{{that is}}		% use Latin or English?  Decide later.
\newcommand{\cf}{{\em cf.}}

%%%%%%%%%%%%%%% Evolution operators, zetas %%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\evOper}{evolution oper\-ator}
\newcommand{\EvOper}{Evolution oper\-ator}
\newcommand{\FPoper}{Perron-Frobenius oper\-ator} % Pesin's ordering
\newcommand{\FP}{Perron-Frobenius}
\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{\qS}{semi\-classical 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}{class\-ic\-al spec\-tral det\-er\-mi\-nant}
\newcommand{\cycForm}{cycle averaging formula}
\newcommand{\CycForm}{Cycle averaging formula}

%%%%%%%%%%%%%%% Sundry symbols within math eviron.: %%%%%%%%%%%%
\newcommand{\DiffConst}{D}
\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{\integers}{\mathbb{Z}}
\newcommand{\rationals}{\mathbb{Q}}
\newcommand{\naturals}{\mathbb{N}}
\newcommand{\LieD}{{{\mathcal 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}{{\rm tr}\, }
\newcommand{\Tr}{\mbox{Tr}\,}
\newcommand{\sign}[1]{{\rm sign}(#1)}
\newcommand{\msr}{{\mu}}		        % 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{\Fqm}{F_{qm}}
\newcommand{\zfct}[1]{\zeta ^{-1}_{#1}}     
\newcommand{\zetatop}{1/\zeta_{\mbox{\footnotesize top}}}
\newcommand{\expct}    [1]{\left\langle {#1} \right\rangle}
\newcommand{\spaceAver}[1]{\left\langle {#1} \right\rangle}
\newcommand{\timeAver} [1]{\overline{#1}}
\newcommand{\pS}{{\mathcal M}}			% symbol for phase space 
\newcommand{\intM}[1]{{\int_\pS{\!d #1}\:}}	%phasespace integral
\newcommand{\PoincS}{{\mathcal P}}			% symbol for Poincare section 
\newcommand{\Lop}{{\mathcal L}}	   % evolution operator
%\newcommand{\Lop}{{\bf L}}	   % evolution operator
\newcommand{\Uop}{{\mathcal U}}	   % Koopman operator
\newcommand{\Aop}{{\mathcal A}}	   % evolution generator
\newcommand{\Top}{{\mathcal T}}	   % transfer operator, like in statmech
\newcommand{\jMps}{{\bf J}}	   %jacobiam matrix, full phase space
\newcommand{\oneMinJ}[1]{\left|\det\left({\bf 1}-{\bf J}_p^{#1}\right)\right|}
				   %Fredholm det jacobian weight
\newcommand{\monodromy}{{\bf J}}   %monodromy matrix, full Poincare cut
\newcommand{\maslov}[1]{{m_{#1}}}  %Maslov index
\newcommand{\ExpaEig}{\Lambda}	   
%\newcommand{\eigenvL}{{s}}	   
\newcommand{\eigenvL}{{\nu}}       %This is really eigenvalue, not log!
\newcommand{\eigCond}{F}           % eigenvalue cond. function
\newcommand{\inFix}[1]{{\in \mbox{\footnotesize Fix}f^{#1}}}
\newcommand{\inZero}[1]{{\in \mbox{\footnotesize Zero} \, f^{#1} }}
\newcommand{\xzero}[1]{{x_{#1}^{*}}}

\newcommand{\eps} {\varepsilon}
\newcommand{\twopi}{{2\pi}}
\newcommand{\avert}[1]{\overline{#1}}
\newcommand{\averx}{\int dx\,}
\newcommand{\derJ}{{d~\over dJ}}

%%%%%%%%%% flows: %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\flow[2]{{f^{#1}(#2)}}
\newcommand\xInit{{x_0}}		%initial x
\newcommand\pSpace{x}		% phase space x=(q,p) coordinate
\newcommand{\para}{\parallel}

%%%%%%%%%%%%%%%% periods: %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\period[1]{{T_{#1}}}			%continuous cycle period
\newcommand{\cl}[1]{{n_{#1}}}	% discrete length of a cycle, Predrag
\newcommand{\timeSegm}[1]{{\tau_{#1}}}		%billiard segment time period
\newcommand\Lyap{\lambda}			%Lyapunov exponent
\newcommand{\dz}{{\delta z}}

%%%%%%%%%%%%%%% 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}{{p_1+p_2+\dots+p_k}}
\newcommand{\block}[1]{#1}
\newcommand{\Ksym}[1]{\sigma_{#1}}
\newcommand{\Ssym}[1]{{s_{#1}}}


%\newcommand{\F}{{\mathcal F}}
% \newcommand{\spao}[1]{\mbox{\hspace{#1}}}
% \newcommand{\spav}[1]{\parbox{1mm}{\vspace*{#1}}}
% \newcommand{\TTeject}{\vspace{1cm}}
%\newcommand{\sign}[1]{{\rm sign}[{#1}]}
	%sign redefined to have square brackets here...

