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

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

1998-05-20

arxiv.org/abs/math-ph/9805019v1

Physics

Mathematical Physics

26 pages, 1 small figure

Scientific paper

10.1088/0951-7715/12/3/002

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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