Ruelle zeta function at zero for surfaces
Dynamical Systems
2017-04-17 v3 Analysis of PDEs
Spectral Theory
Abstract
We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously known only in constant curvature.
Cite
@article{arxiv.1606.04560,
title = {Ruelle zeta function at zero for surfaces},
author = {Semyon Dyatlov and Maciej Zworski},
journal= {arXiv preprint arXiv:1606.04560},
year = {2017}
}
Comments
17 pages. Added Remark 2 on page 1 and revised following the referee's suggestions. To appear in Inventiones Mathematicae