Decidability of chaos for some families of dynamical systems

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We show that existence of positive Lyapounov exponents and/or SRB measures are undecidable (in the algorithmic sense) properties within some parametrized families of interesting dynamical systems: quadratic family and Hénon maps. Because the existence of positive exponents (or SRB measures) is, in a natural way, a manifestation of ``chaos'', these results may be understood as saying that the chaotic character of a dynamical system is undecidable. Our investigation is directly motivated by questions asked by Carleson and Smale in this direction.
7 pages

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Dynamical Systems, 37C99;03D35

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http://salesiana.dossiersoluciones.com/handle/123456789/65913

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0212101
 http://arxiv.org/abs/math/0212101

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arXiv