Exact Lyapunov Dimension of the Universal Attractor for the Complex Ginzburg-Landau Equation

Charles R. Doering; John D. Gibbon; Darryl D. Holm; Basil Nicolaenko

doi:10.1103/PhysRevLett.59.2911

Exact Lyapunov Dimension of the Universal Attractor for the Complex Ginzburg-Landau Equation

Charles R. Doering, John D. Gibbon, Darryl D. Holm, and Basil Nicolaenko

Phys. Rev. Lett. 59, 2911 – Published 28 December 1987

Abstract

We present an exact analytic computation of the Lyapunov dimension of the universal attractor of the complex Ginzburg-Landau partial differential equation for a finite range of its parameter values. We obtain upper bounds on the attractor's dimension when the parameters do not permit an exact evaluation by our methods. The exact Lyapunov dimension agrees with an estimate of the number of degrees of freedom based on a simple linear stability analysis and mode-counting argument.

Received 16 September 1987

DOI:https://doi.org/10.1103/PhysRevLett.59.2911

Authors & Affiliations

Charles R. Doering^*, John D. Gibbon^†, Darryl D. Holm, and Basil Nicolaenko

Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

^*Permanent address: Department of Physics, Clarkson University, Potsdam, NY 13676.
^†Permanent address: Department of Mathematics, Imperial College, London, England.