Abstract : We consider the dynamical behavior of Martin-Löf random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic model for the dynamics. Through this construction we prove that such points have typical statistical behavior (the behavior which is typical in the Birkhoff ergodic theorem) and are recurrent. We introduce and compare some notions of complexity for orbits in dynamical systems and prove: (i) that the complexity of the orbits of random points equals the Kolmogorov-Sinaï entropy of the system, (ii) that the supremum of the complexity of orbits equals the topological entropy.
https://hal.inria.fr/inria-00517382
Contributeur : Mathieu Hoyrup
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Soumis le : mardi 14 septembre 2010 - 14:33:19
Dernière modification le : jeudi 11 janvier 2018 - 06:21:25
Document(s) archivé(s) le : mardi 23 octobre 2012 - 16:11:12
