98-353 Collet P., Eckmann J.-P.

The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's (291K, postcript) May 20, 98

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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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