Mathematical analysis/Dynamical systems
Ruelle operators and decay of correlations for contact Anosov flows
Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 669-672.

We prove strong spectral estimates for Ruelle transfer operators for arbitrary C2 contact Anosov flows. As a consequence of this we obtain: (a) existence of a non-zero analytic continuation of the Ruelle zeta function with a pole at the entropy in a vertical strip containing the entropy in its interior; (b) a Prime Orbit Theorem with an exponentially small error; (c) exponential decay of correlations for Hölder continuous observables with respect to any Gibbs measure.

On prouve des estimations spectrales fortes pour lʼopérateur de transfert de Ruelle relatif à des flots de contact dʼAnosov arbitraires de classe C2. Comme conséquence, on obtient les trois résultats suivants : (a) lʼexistence dʼun prolongement analytique sans zéros de la fonction zêta de Ruelle dans une bande verticale contenant lʼentropie dans son intérieur et ayant lʼentropie comme ensemble de pôles ; (b) un théorème asymptotique pour le nombre de trajectoires périodiques primitives avec un reste exponentiellement petit ; (c) la décroissance exponentielle des corrélations pour des observables höldériennes par rapport à une mesure de Gibbs quelconque.

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Accepted:
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DOI: 10.1016/j.crma.2013.09.012
Stoyanov, Luchezar 1

1 University of Western Australia, School of Mathematics and Statistics, Perth, WA 6009, Australia
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Stoyanov, Luchezar. Ruelle operators and decay of correlations for contact Anosov flows. Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 669-672. doi : 10.1016/j.crma.2013.09.012. http://www.numdam.org/articles/10.1016/j.crma.2013.09.012/

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