Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiards
[Bornes polynomiales précises pour la décroissance des corrélations d’applications non-uniformément hyperboliques en plusieurs dimensions et de billards]
Annales Henri Lebesgue, Tome 4 (2021), pp. 407-451.

Gouëzel et Sarig ont introduit la théorie du renouvellement d’opérateurs pour démontrer des résultats précis sur la décroissance des corrélations dans certaines classes d’applications non-uniformément dilatantes. Dans cet article, nous appliquons cette méthode à des billards plans dispersifs et des applications intermittentes non-markoviennes en plusieurs dimensions.

Gouëzel and Sarig introduced operator renewal theory as a method to prove sharp results on polynomial decay of correlations for certain classes of nonuniformly expanding maps. In this paper, we apply the method to planar dispersing billiards and multidimensional nonMarkovian intermittent maps.

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DOI : 10.5802/ahl.76
Classification : 37A25, 37D25, 37D50, 60K05
Mots clés : Sharp mixing rates, nonuniform hyperbolicity, billiards, multidimensional intermittent maps, operator renewal theory
Bruin, Henk 1 ; Melbourne, Ian 2 ; Terhesiu, Dalia 3

1 Faculty of Mathematics, University of Vienna, 1090 Vienna, (Austria)
2 Mathematics Institute, University of Warwick, Coventry, CV4 7AL, (UK)
3 Mathematisch Instituut, Niels Bohrweg 1, 2333 CA Leiden, (The Netherlands)
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Bruin, Henk; Melbourne, Ian; Terhesiu, Dalia. Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiards. Annales Henri Lebesgue, Tome 4 (2021), pp. 407-451. doi : 10.5802/ahl.76. http://archive.numdam.org/articles/10.5802/ahl.76/

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