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The purpose of this paper is to give a short microlocal proof of the meromorphic continuation of the Ruelle zeta function for Anosov flows. More general results have been recently proved by Giulietti-Liverani-Pollicott [13] but our approach is different and is based on the study of the generator of the flow as a semiclassical differential operator.
Cet article donne une courte preuve microlocale du prolongement méromorphe de la fonction zêta de Ruelle pour les flots d'Anosov lisses. Des résultats plus généraux ont été récemment obtenus par Giulietti-Liverani-Pollicott [13] mais notre approche est différente et se base sur l'étude du générateur du flot, que l'on considère comme un opérateur pseudodifférentiel semi-classique.
@article{ASENS_2016__49_3_543_0,
author = {Dyatlov, Semyon and Zworski, Maciej},
title = {Dynamical zeta functions for {Anosov} flows via microlocal analysis},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {543--577},
publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
volume = {Ser. 4, 49},
number = {3},
year = {2016},
doi = {10.24033/asens.2290},
zbl = {1369.37028},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.24033/asens.2290/}
}
TY - JOUR AU - Dyatlov, Semyon AU - Zworski, Maciej TI - Dynamical zeta functions for Anosov flows via microlocal analysis JO - Annales scientifiques de l'École Normale Supérieure PY - 2016 SP - 543 EP - 577 VL - 49 IS - 3 PB - Société Mathématique de France. Tous droits réservés UR - http://geodesic.mathdoc.fr/articles/10.24033/asens.2290/ DO - 10.24033/asens.2290 LA - en ID - ASENS_2016__49_3_543_0 ER -
%0 Journal Article %A Dyatlov, Semyon %A Zworski, Maciej %T Dynamical zeta functions for Anosov flows via microlocal analysis %J Annales scientifiques de l'École Normale Supérieure %D 2016 %P 543-577 %V 49 %N 3 %I Société Mathématique de France. Tous droits réservés %U http://geodesic.mathdoc.fr/articles/10.24033/asens.2290/ %R 10.24033/asens.2290 %G en %F ASENS_2016__49_3_543_0
Dyatlov, Semyon; Zworski, Maciej. Dynamical zeta functions for Anosov flows via microlocal analysis. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 3, pp. 543-577. doi : 10.24033/asens.2290. http://geodesic.mathdoc.fr/articles/10.24033/asens.2290/
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