Dynamical zeta functions for Anosov flows via microlocal analysis

Abstract

The purpose of this paper is to give a short microlocal proof of the meromorphic continuation of the Ruelle zeta function for C^\infty Anosov flows. More general results have been recently proved by Giulietti-Liverani-Pollicott [arXiv:1203.0904] but our approach is different and is based on the study of the generator on the flow as a semiclassical differential operator.

arXiv comment38 pages, 3 figures; one more minor correction at the end of Section 3.1. To appear in Annales de l'ENS