Numerical computation of ε-entropy for parabolic equations with analytic solutions

G. J. Lord, J. Rougemont

Research output: Contribution to journalArticlepeer-review


We report on numerical experiments computing the e-entropy for parabolic partial differential equations. The e-entropy is a measure of the spatial density of complexity for the dynamics on an invariant set in function space and has been studied analytically by a number of authors. The e-entropy only requires solutions of the equation to the accuracy of the parameter e and the resulting number is (asymptotically) independent of domain size. We consider the complex Ginzburg-Landau equation as an example where a number of analytic results exist and the Kuramoto-Sivashinsky equation where the accompanying theory has yet to be fully developed. Our numerical results for the Kuramoto-Sivashinsky equation do not contradict the conjectured linear scaling of the dimension with domain size. © 2004 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)65-74
Number of pages10
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
Publication statusPublished - 1 Jul 2004


  • ε-Entropy
  • Attractor
  • Dimension
  • Gevrey regularity


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