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.
Accepté le :
Publié le :
DOI : 10.5802/jep.107
Keywords: Ruelle resonances, pseudo-Anosov, linear flow; cohomological equation
Mot clés : Résonances de Ruelle, pseudo-Anosov, flot linéaire, équation cohomologique
@article{JEP_2019__6__811_0, author = {Faure, Fr\'ed\'eric and Gou\"ezel, S\'ebastien and Lanneau, Erwan}, title = {Ruelle spectrum of linear {pseudo-Anosov} maps}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {811--877}, publisher = {Ecole polytechnique}, volume = {6}, year = {2019}, doi = {10.5802/jep.107}, zbl = {07114039}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jep.107/} }
TY - JOUR AU - Faure, Frédéric AU - Gouëzel, Sébastien AU - Lanneau, Erwan TI - Ruelle spectrum of linear pseudo-Anosov maps JO - Journal de l’École polytechnique — Mathématiques PY - 2019 SP - 811 EP - 877 VL - 6 PB - Ecole polytechnique UR - http://www.numdam.org/articles/10.5802/jep.107/ DO - 10.5802/jep.107 LA - en ID - JEP_2019__6__811_0 ER -
%0 Journal Article %A Faure, Frédéric %A Gouëzel, Sébastien %A Lanneau, Erwan %T Ruelle spectrum of linear pseudo-Anosov maps %J Journal de l’École polytechnique — Mathématiques %D 2019 %P 811-877 %V 6 %I Ecole polytechnique %U http://www.numdam.org/articles/10.5802/jep.107/ %R 10.5802/jep.107 %G en %F JEP_2019__6__811_0
Faure, Frédéric; Gouëzel, Sébastien; Lanneau, Erwan. Ruelle spectrum of linear pseudo-Anosov maps. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 811-877. doi : 10.5802/jep.107. http://www.numdam.org/articles/10.5802/jep.107/
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