Pollicott-Ruelle resonances for open systems
Dynamical Systems
2016-05-03 v2 Analysis of PDEs
Abstract
We define Pollicott-Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems related to Axiom A flows. These resonances are the poles of the meromorphic continuation of the resolvent of the generator of the flow and they describe decay of classical correlations. As an application, we show that the Ruelle zeta function extends meromorphically to the entire complex plane.
Cite
@article{arxiv.1410.5516,
title = {Pollicott-Ruelle resonances for open systems},
author = {Semyon Dyatlov and Colin Guillarmou},
journal= {arXiv preprint arXiv:1410.5516},
year = {2016}
}
Comments
59+eps pages, 10 figures; several localized changes in response to referee's comments. To appear in Annales Henri Poincar\'e