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Article Dans Une Revue International journal of bifurcation and chaos in applied sciences and engineering Année : 2010

On the statistical distribution of first-return times of balls and cylinders in chaotic systems

Résumé

We study returns in dynamical systems: when a set of points, initially populating a prescribed region, swarms around phase space according to a deterministic rule of motion, we say that the return of the set occurs at the earliest moment when one of these points comes back to the original region. We describe the statistical distribution of these "first return" times in various setting: when phase space is composed of sequences of symbols from a finite alphabet (with application for instance to bilogical problems) and when phase space is a one and two-dimensional manifold. Specifically, we consider Bernoulli shifts, expanding maps of the interval and linear automorphisms of the two dimensional torus. we decscribe relations linking these statistics with Rényi entropies and Lyapunov exponents.
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Dates et versions

hal-00476239 , version 1 (25-04-2010)

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Sandro Vaienti, Giorgio Mantica. On the statistical distribution of first-return times of balls and cylinders in chaotic systems. International journal of bifurcation and chaos in applied sciences and engineering , 2010, 20 (6), pp.1845. ⟨10.1142/S0218127410026897⟩. ⟨hal-00476239⟩
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