Ruelle spectrum of linear pseudo-Anosov maps

Frédéric Faure; Sébastien Gouëzel; Erwan Lanneau

doi:10.5802/jep.107

Ruelle spectrum of linear pseudo-Anosov maps
[Spectre de Ruelle des applications pseudo-Anosov linéaires]

Frédéric Faure ¹ ; Sébastien Gouëzel ² ; Erwan Lanneau ¹

¹ Univ. Grenoble Alpes, CNRS UMR 5582, Institut Fourier F-38000 Grenoble, France
² Laboratoire Jean Leray, CNRS UMR 6629, Université de Nantes 2 rue de la Houssinière, 44322 Nantes, France

Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 811-877.

Résumé
Abstract

Les résonances de Ruelle d’un système dynamique sont des données spectrales qui décrivent les asymptotiques précises des corrélations. Nous les classifions complètement pour une classe d’applications chaotiques en dimension deux, les applications pseudo-Anosov linéaires, en termes de l’action en cohomologie de la transformation. Nous en déduisons une description complète des distributions qui sont invariantes par le flot linéaire dans la direction stable d’un tel pseudo-Anosov, et nous résolvons l’équation cohomologique pour ce flot.

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.

Reçu le : 2018-12-18
Accepté le : 2019-07-16
Publié le : 2019-09-24

Zbl

DOI : 10.5802/jep.107

Classification : 37D50, 37A25
Keywords: Ruelle resonances, pseudo-Anosov, linear flow; cohomological equation
Mot clés : Résonances de Ruelle, pseudo-Anosov, flot linéaire, équation cohomologique

Affiliations des auteurs :

Frédéric Faure ¹ ; Sébastien Gouëzel ² ; Erwan Lanneau ¹

¹ Univ. Grenoble Alpes, CNRS UMR 5582, Institut Fourier F-38000 Grenoble, France
² Laboratoire Jean Leray, CNRS UMR 6629, Université de Nantes 2 rue de la Houssinière, 44322 Nantes, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Fr\'ed\'eric Faure and S\'ebastien Gou\"ezel and Erwan Lanneau},
     title = {Ruelle spectrum of linear {pseudo-Anosov} maps},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {811--877},
     publisher = {\'Ecole polytechnique},
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Frédéric Faure; Sébastien Gouëzel; Erwan Lanneau. Ruelle spectrum of linear pseudo-Anosov maps. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 811-877. doi : 10.5802/jep.107. https://jep.centre-mersenne.org/articles/10.5802/jep.107/

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