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arXiv · 1808.00202

Ruelle spectrum of linear pseudo-Anosov maps

Frédéric Faure·Sébastien Gouëzel·Erwan Lanneau
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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.

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Frédéric Faure, Sébastien Gouëzel, Erwan Lanneau. 2018-08-01. Ruelle spectrum of linear pseudo-Anosov maps. https://arxiv.org/abs/1808.00202

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