Ruelle operators and decay of correlations for contact Anosov flows

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    Abstract

    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. © 2013 Académie des sciences.
    Original languageEnglish
    Pages (from-to)669-672
    JournalACADEMIE DES SCIENCES. COMPTES RENDUS. MATHEMATIQUE
    Volume351
    Issue number17-16
    DOIs
    Publication statusPublished - 2013

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