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

P. Collet·J. -P. Eckmann
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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.

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P. Collet, J. -P. Eckmann. 1998-05-20. The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's. https://doi.org/10.1088/0951-7715%2F12%2F3%2F002

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