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Decidability of chaos for some families of dynamical systems

Alexander Arbieto·Carlos Matheus
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Abstract

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.

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Alexander Arbieto, Carlos Matheus. 2003-02-24. Decidability of chaos for some families of dynamical systems. https://arxiv.org/abs/math/0212101

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