Dynamical zeta functions for Anosov flows via microlocal analysis
Dynamical Systems
2016-05-06 v4 Analysis of PDEs
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1306.4203,
title = {Dynamical zeta functions for Anosov flows via microlocal analysis},
author = {Semyon Dyatlov and Maciej Zworski},
journal= {arXiv preprint arXiv:1306.4203},
year = {2016}
}
Comments
38 pages, 3 figures; one more minor correction at the end of Section 3.1. To appear in Annales de l'ENS