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Lyapunov exponents and rates of mixing for one-dimensional maps

By José F. Alves, Stefano Luzzatto and Vilton Pinheiro


We show that one dimensional maps f with strictly positive Lyapunov exponents almost everywhere admit an absolutely continuous invariant measure. If f is topologically transitive some power of f is mixing and in particular the correlation of Hölder continuous observables decays to zero. The main objective of this paper is to show that the rate of decay of correlations is determined, in some situations, to the average rate at which typical points start to exhibit exponential growth of the derivative

Year: 2002
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