Mathematics > Dynamical Systems
[Submitted on 21 Jul 2010]
Title:From Rates of mixing to recurrence times via large deviations
View PDFAbstract: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.
Submission history
From: Jorge Milhazes Freitas [view email][v1] Wed, 21 Jul 2010 22:39:45 UTC (31 KB)
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