Growth and mixing

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Given a bi-Lipschitz measure-preserving homeomorphism of a compact metric measure space of finite dimension, consider the sequence formed by the Lipschitz norms of its iterations. We obtain lower bounds on the growth rate of this sequence assuming that our homeomorphism mixes a Lipschitz function. In particular, we get a universal lower bound which depends on the dimension of the space but not on the rate of mixing. Furthermore, we get a lower bound on the growth rate in the case of rapid mixing. The latter turns out to be sharp: the corresponding example is given by a symbolic dynamical system associated to the Rudin-Shapiro sequence.
To appear in Journal of Modern Dynamics

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Dynamical Systems, 37A05, 37A25, 37C05

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http://salesiana.dossiersoluciones.com/handle/123456789/215335

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.0954
 http://arxiv.org/abs/0706.0954

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arXiv