A family of chaotic billiards with variable mixing rates

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We describe a one-parameter family of dispersing (hence hyperbolic, ergodic and mixing) billiards where the correlation function of the collision map decays as $1/n^a$ (here $n$ denotes the discrete time), in which the degree $a \in (1, \infty)$ changes continuously with the parameter of the family, $β$. We also derive an explicit relation between the degree $a$ and the family parameter $β$.
23 page, 7 figures

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Mathematical Physics, Dynamical Systems, 37D50, 37A25

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http://salesiana.dossiersoluciones.com/handle/123456789/57817

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0409024
 http://arxiv.org/abs/math-ph/0409024

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arXiv