The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's
Collet, P. ; Eckmann, J. -P.
arXiv, 9805019 / Harvested from arXiv
Text on arXiv
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.
Publié le : 1998-05-20
Classification:  Mathematical Physics,  Mathematics - Dynamical Systems 
@article{9805019,
     author = {Collet, P. and Eckmann, J. -P.},
     title = {The Definition and Measurement of the Topological Entropy per Unit
  Volume in Parabolic PDE's},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9805019}
}

Collet, P.; Eckmann, J. -P. The Definition and Measurement of the Topological Entropy per Unit
  Volume in Parabolic PDE's. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9805019/