Decay of correlations for nonuniformly expanding systems
Bulletin de la Société Mathématique de France, Volume 134 (2006) no. 1, p. 1-31

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 ).

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 ).

DOI : https://doi.org/10.24033/bsmf.2500
Classification:  37A25,  37D25
Keywords: decay of correlations, Young tower, non uniformly expanding maps
@article{BSMF_2006__134_1_1_0,
     author = {Gou\"ezel, S\'ebastien},
     title = {Decay of correlations for nonuniformly expanding systems},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {134},
     number = {1},
     year = {2006},
     pages = {1-31},
     doi = {10.24033/bsmf.2500},
     mrnumber = {2233699},
     zbl = {1111.37018},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2006__134_1_1_0}
}
Gouëzel, Sébastien. Decay of correlations for nonuniformly expanding systems. Bulletin de la Société Mathématique de France, Volume 134 (2006) no. 1, pp. 1-31. doi : 10.24033/bsmf.2500. http://www.numdam.org/item/BSMF_2006__134_1_1_0/

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