Ruelle spectrum of linear pseudo-Anosov maps
Dynamical Systems
2018-08-02 v1
Abstract
The Ruelle resonances of a dynamical system are spectral data describing the precise asymptotics of correlations. We classify them completely for a class of chaotic two-dimensional maps, the linear pseudo-Anosov maps, in terms of the action of the map on cohomology. As applications, we obtain a full description of the distributions which are invariant under the linear flow in the stable direction of such a linear pseudo-Anosov map, and we solve the cohomological equation for this flow.
Keywords
Cite
@article{arxiv.1808.00202,
title = {Ruelle spectrum of linear pseudo-Anosov maps},
author = {Frédéric Faure and Sébastien Gouëzel and Erwan Lanneau},
journal= {arXiv preprint arXiv:1808.00202},
year = {2018}
}