[Décroissance des corrélations d'un système non uniformément dilatant]
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
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
Keywords: decay of correlations, Young tower, non uniformly expanding maps
Mot clés : décroissance des corrélations, tour de Young, applications non uniformément dilatantes
@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}, pages = {1--31}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {134}, number = {1}, year = {2006}, doi = {10.24033/bsmf.2500}, zbl = {1111.37018}, mrnumber = {2233699}, language = {en}, url = {https://www.numdam.org/articles/10.24033/bsmf.2500/} }
TY - JOUR AU - Gouëzel, Sébastien TI - Decay of correlations for nonuniformly expanding systems JO - Bulletin de la Société Mathématique de France PY - 2006 SP - 1 EP - 31 VL - 134 IS - 1 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2500/ DO - 10.24033/bsmf.2500 LA - en ID - BSMF_2006__134_1_1_0 ER -
%0 Journal Article %A Gouëzel, Sébastien %T Decay of correlations for nonuniformly expanding systems %J Bulletin de la Société Mathématique de France %D 2006 %P 1-31 %V 134 %N 1 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2500/ %R 10.24033/bsmf.2500 %G en %F BSMF_2006__134_1_1_0
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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