The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's

Abstract

We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows (in principle) to measure this entropy from experimental data.

arXiv comment26 pages, 1 small figure

References in corpus (2)

• Extensive Properties of the Complex Ginzburg-Landau Equation
• Thermodynamic Limit Of The Ginzburg-Landau Equations

Cited by in corpus (5)

• Predictability: a way to characterize Complexity
• Space-Time Complexity in Hamiltonian Dynamics
• A quasi-diagonal approach to the estimation of Lyapunov spectra for spatio-temporal systems from multivariate time series
• Complexity for extended dynamical systems
• Behavior of solutions and chaos in nonlinear reaction-diffusion PDE's related to cancer