% refs.tex                           NSF Appl Math proposal

% Marsha                                Nov  3 2003
% Predrag                               Nov  2 2003

\begin{thebibliography}{999}

\bibitem{Hopf48} E. Hopf,
        ``A mathematical example displaying features of turbulence,"
        {\em Commun. Appl. Math. \bf 1}, 303 (1948). % , 303-322.

\bibitem{KurSiv}
% \bibitem{Kur}
    Y. Kuramoto and T. Tsuzuki,
    ``Persistent propagation of concentration waves in
          dissipative media far from thermal equilibrium,"
    {\em Progr. Theor. Physics \bf 55}, 365 (1976);
% \bibitem{Siv}
    G.I. Sivashinsky,
   ``Nonlinear analysis of hydrodynamical instability
            in laminar flames --- I. Derivation of basic equations,"
    {\em Acta Astr. \bf 4}, 1177 (1977).

\bibitem{CCP96} F. Christiansen, P. Cvitanovi\'c, and V. Putkaradze,
    ``Spatiotemporal chaos in terms of unstable recurrent patterns,"
    {\em Nonlinearity} {\bf 10}, 1 (1997);
    {\tt chao-dyn/9606016}.

\bibitem{Foias88} See, for ex.,
        C.~Foias, B.~Nicolaenko, G.~R.~Sell and R.~T\'emam,
        {``Kuramoto-Sivashinsky equation''},
        {\em J.~Math. Pures et Appl. \bf 67}, 197 (1988).

\bibitem{FST86} U. Frisch, Z.~Su~She and O.~Thual,
        ``Viscoelastic behaviour of cellular solutions to the
        Kuramoto-Shivashinsky model,"
        {\em J. Fluid Mech. \bf 168}, 221 (1986). % 221-240

\bibitem{landau44} L.D. Landau,
    ``On the problem of turbulence,"
    {\em Akad. Nauk. Doklady \bf 44}, 339 (1944).

\bibitem{rue_tak} D. Ruelle and F. Takens,
    {``On the nature of turbulence"},
       {\em Commun. Math. Phys. \bf 20}, 167 (1971).

\bibitem{QCcourse}
P. Cvitanovi\'c {\em et al.},
{\em  Chaos: Classical and Quantum},
advanced graduate e-textbook, available
online at {\tt ChaosBook.org}
    (Niels Bohr Institute, Copenhagen 2003).

\bibitem{JY02} J. Yen,
    ``Life in transition: balancing inertial and viscous forces by
planktonic copepods,"
    {\em  Biol. Bull. \bf 198}, 213 (2000). %213-224

\bibitem{evap} R.O. Grigoriev and A. Handel,
   ``Spectral Theory for the Failure of Linear Control
    in a Nonlinear Stochastic System,"
    {\it Phys. Rev. \bf E 66}, 065301 (2002).

\bibitem{HopfsLastSrc} According to E.A.~Spiegel~\cite{MS66}, %,EAS87},
who has pioneered study of turbulence in terms of unstable
periodic solutions.
We have not been able to identify the reference {\em in which}
E.~Hopf wrote this down.

\bibitem{MS66} D.W. Moore and  E.A. Spiegel,
       ``A thermally excited nonlinear oscillator,"
       {\em Astrophys. J., \bf 143}, 871 (1966); %.
%
%\bibitem{EAS87}
    E.A.~Spiegel,
        ``Chaos: a mixed metaphor for turbulence,"
        {\em Proc. Roy. Soc. \bf A413}, 87 (1987).


\bibitem{crete03}
        P.~Cvitanovi\'c and Y.~Lan,
        {``Turbulent fields and their recurrences''},
        in N.~Antoniou, ed.,
        {\em Proceed. of
        10. Intern. Workshop on Multiparticle Production:
        Correlations and Fluctuations in QCD
        }
        (World Scientific, Singapore 2003);
        % submitted (March 2003)
        {\tt nlin.CD/0308006}.

\bibitem{LanDescent} Y.~Lan and P.~Cvitanovi\'c,
        ``Variational method for finding periodic orbits
        in a general flow,''
        {\em Phys. Rev. \bf E} (2003), to appear;
         {\tt nlin.CD/0308008}.

\bibitem{Onsager53} L.~Onsager and  S.~Machlup,
         {\em Phys. Rev. \bf 91}, 1505, 1512 (1953).

%numerical and experimental attempts
\bibitem{auerbach} D. Auerbach, P. Cvitanovi\'c, J.-P. Eckmann,
G.H. Gunaratne and I. Procaccia,
        \Journal{\em Phys. Rev. Lett.}{58}{2387}{1987}.
        %{\em Phys. Rev. Lett. \bf 58}, 2387 (1987).

\bibitem{HLB96} P. Holmes, J.L. Lumley and G. Berkooz,
        {\em Turbulence, Coherent Structures,
        Dynamical Systems and Symmetry}
        (Cambridge U. Press, Cambridge 1996).

\bibitem{ZG96} S.M. Zoldi and H.S. Greenside,
       ``Spatially localized unstable periodic orbits
         of a high-dimensional chaotic system,"
        {\em Phys. Rev. \bf E 57} (1998) R2511. % R2511-R2514

\bibitem{Waleffe2003} F.~Waleffe,       % Fabian
        ``Homotopy of exact coherent structures in plane shear flows,''
        {\em Phys. Fluids, \bf 15}, 1517 (2003).

\bibitem{KawKida01} G. Kawahara and S. Kida,
``Periodic motion embedded in plane Couette turbulence: regeneration cycle
and burst,''
{\it  J. Fluid Mech.} {\bf449},  291 (2001). % pp. 291-300

\bibitem{PG97} P. Gaspard,
        ``Chaos, Scattering and Statistical Mechanics''
        (Cambridge Univ. Press, Cambridge 1997).

\bibitem{CEflows} P. Cvitanovi\'c and  B. Eckhardt,
        ``Periodic orbit expansions for classical smooth flows,"
    {\em J. Phys. \bf A 24}, L237 (1991).

\bibitem{Rugh92} H.H. Rugh,
        ``The Correlation Spectrum for Hyperbolic Analytic Maps,"
    {\em Nonlinearity \bf 5} (1992) 1237.

\bibitem{CNS} Center for Nonlinear Science,
    {\tt www.cns.gatech.edu}.


\bibitem{Hexagon} D. Semwogerere and  M.F. Schatz,
   ``Evolution of hexagonal patterns
      from controlled initial conditions in a
      B\'{e}nard-Marangoni convection experiment,"
    {\em Phys. Rev. Lett.} {\bf 88}, (2002).
\PC{find page number in \refref{Hexagon}}

% \bibitem{GGS03} N. Garnier, R.O. Grigoriev, and M.F. Schatz,
%   ``Optical manipulation of microscale fluid flow,"
%    {\em  Phys. Rev. Lett.},  (2003).
%\PC{find page number in \refref{GGS03}}

\bibitem{MezSat02} I. Mezi\'c and F. Sotiropoulos,
    ``Ergodic Theory and Experimental
     Visualization of Invariant Sets in Chaotically Advected Flows,''
    {\em Physics of Fluids \bf 14}, 2235 (2002). %2235-2243.

\bibitem{LGC02} Y.~Lan, P.~Cvitanovi\'c and N.~Garnier,
    ``Stationary modulated-amplitude waves in
    the 1-D complex Ginzburg-Landau equation.''
    % (with Y.~ Lan and N.~Garnier)
    {\em Physica \bf D } (2003), to appear;
        {\tt nlin.PS/0208001}.

\bibitem{BECprl} M.A.~Porter and P.~Cvitanovi\'c,
    ``Modulated Amplitude Waves in Bose-Einstein Condensates,''
    %(with M.A.~Porter)
    {\em Phys. Rev. \bf E} (2003), to appear;
        {\tt nonlin.CD/0307032}.

\bibitem{BEC-CHAOS}  M.A.~Porter and P.~Cvitanovi\'c,
        ``A Perturbative Analysis of Modulated Amplitude Waves in Bose-Einstein Condensates,''
        %(with M.A.~Porter)
        {\em CHAOS} (2003), to appear;
        {\tt nlin.CD/0308024}.

\bibitem{Dettm03} C.P. Dettmann,
    ``Fractal asymptotics,''
      {\em Physica \bf D} (2003),   to appear.

\bibitem{pd}   M.J. Feigenbaum,
   {\it J. Stat.\ Phys.\ }{\bf 19}, 25 (1978);
   {\bf 21}, 669 (1979).


%%%%%%%%%%%% General links %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\bibitem{nonnor} R.O. Grigoriev and A. Handel,
    ``Nonnormality and the localized control of extended systems,"
    {\em  Phys. Rev. \bf E 66}, 067201 (2002).






\end{thebibliography}

% \bibitem{DWebster03} D.~Webster, (unpublished), simulation videos available on
%   \\
%         {\tt www.ce.gatech.edu/$\sim$dwebster}
%
