Anosov flows and dynamical zeta functions

By P. Giulietti, C. Liverani, Mark Pollicott. 2012

152 citations recorded by the source corpus.

We study the Ruelle and Selberg zeta functions for C r Anosov ows, r > 2, on a compact smooth manifold. We prove several results, the most remarkable being (a) for C 1 ows the zeta function is meromorphic on the entire complex plane; (b) for contact ows satisfying a bunching condition (e.g., geodesic ows on manifolds of negative curvature better than 1 9 -pinched), the zeta function has a pole at the topological entropy and is analytic in a strip to its left; (c) under the same hypotheses as in (b) we obtain sharp results on the number of periodic orbits. Our arguments are based on the study of the spectral properties of a transfer operator acting on suitable Banach spaces of anisotropic currents.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/207b2f9466c588f94b88e31ec61995ae18847a8d

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Dynamical zeta functions for Anosov flows via microlocal analysis (2013, background): “ paper is to give a short microlocal proof of the meromorphic continuation of the Ruelle zeta function for C1Anosov ows. More general results have been recently proved by Giulietti{Liverani{Pollicott [GiLiPo] but our approach is dierent and is based on the study of the generator of the ow as a semic”
The semiclassical zeta function for geodesic flows on negatively curved manifolds (2013, background): “Recently, Giulietti, Liverani and Pollicott published a paper [22] on dynamical zeta functions for Anosov flows.”