Decay of correlations for nonuniformly expanding systems
[Décroissance des corrélations d'un système non uniformément dilatant]
Bulletin de la Société Mathématique de France, Tome 134 (2006) no. 1, pp. 1-31.

On montre comment estimer la vitesse de mélange d’un système dynamique non uniformément dilatant, à partir d’estimées sur le temps dont le système a besoin pour être vraiment dilatant. Cette méthode permet d’obtenir des vitesses rapides, par exemple exponentielles gauches ou exponentielles. Comme application, on obtient en particulier le fait que les corrélations des applications d’Alves-Viana décroissent en O(e-cn).

We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. We prove in particular that the correlations of the Alves-Viana map decay in O(e-cn).

DOI : 10.24033/bsmf.2500
Classification : 37A25, 37D25
Keywords: decay of correlations, Young tower, non uniformly expanding maps
Mot clés : décroissance des corrélations, tour de Young, applications non uniformément dilatantes 
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Gouëzel, Sébastien. Decay of correlations for nonuniformly expanding systems. Bulletin de la Société Mathématique de France, Tome 134 (2006) no. 1, pp. 1-31. doi : 10.24033/bsmf.2500. https://www.numdam.org/articles/10.24033/bsmf.2500/

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