Dynamical zeta functions for Anosov flows via microlocal analysis

TL;DR

This paper provides a microlocal analysis-based proof for the meromorphic continuation of the Ruelle zeta function associated with smooth Anosov flows, offering an alternative approach to existing methods.

Contribution

It introduces a novel microlocal proof technique for meromorphic continuation of the Ruelle zeta function using semiclassical differential operator analysis.

Findings

Microlocal proof of meromorphic continuation for Ruelle zeta function

Application of semiclassical analysis to dynamical zeta functions

Alternative approach differing from previous proofs

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.