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Mathematics  2013 

Ruelle transfer operators for contact Anosov flows and decay of correlations

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Abstract:

We prove strong spectral estimates for Ruelle transfer operators for arbitrary $C^2$ contact Anosov flows in any dimension. For such flows some of the consequences of the main result are: (a) exponential decay of correlations for H\"older continuous observables with respect to any Gibbs measure; (b) 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; (c) a Prime Orbit Theorem with an exponentially small error. All these results apply for example to geodesic flows on arbitrary compact Riemann manifolds of negative curvature.

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