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arXiv · 1007.3771

From Rates of mixing to recurrence times via large deviations

José F. Alves·Jorge Milhazes Freitas·Stefano Luzzatto·Sandro Vaienti
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Abstract

A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of correlations. Such geometric structures are generally highly non-trivial and thus a natural question is the extent to which this approach can be applied. In this paper we show that in many cases stochastic-like behaviour itself implies that the system has certain non-trivial geometric properties, which are therefore necessary as well as sufficient conditions for the occurrence of the statistical properties under consideration. As a by product of our techniques we also obtain some new results on large deviations for certain classes of systems which include Viana maps and multidimensional piecewise expanding maps.

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José F. Alves, Jorge Milhazes Freitas, Stefano Luzzatto, Sandro Vaienti. 2010-07-21. From Rates of mixing to recurrence times via large deviations. https://arxiv.org/abs/1007.3771

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