The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE’s
نویسندگان
چکیده
We define the topological entropy per unit volume in parabolic PDE’s such as the complex GinzburgLandau 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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ar X iv : m at h - ph / 9 80 50 19 v 1 2 0 M ay 1 99 8 The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE ’ s
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 allow...
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