Dynamical zeta functions for Anosov flows via microlocal analysis
By Semyon Dyatlov, Maciej Zworski. 2013
188 citations recorded by the source corpus.
The purpose of this paper is to give a short microlocal proof of the meromorphic continuation of the Ruelle zeta function for C^\infty Anosov flows. More general results have been recently proved by Giulietti-Liverani-Pollicott [arXiv:1203.0904] but our approach is different and is based on the study of the generator on the flow as a semiclassical differential operator.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/cf2b8a198a7b81fd9be398871f94be8a3139a032
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In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Invariant distributions and X-ray transform for Anosov flows (2014, unknown): “The microlocal structure (wave-front set) of Π follows directly from the recent work of Dyatlov-Zworski [DyZw], see Proposition 2.”
- The semiclassical zeta function for geodesic flows on negatively curved manifolds (2013, background): “Recently a few papers authored by Datchev, Dyatlov, Nonnenmacher and Zworski gave precise results for contact Anosov flows using this semiclassical approach: spectral gap estimate and decay of correlations [35], Weyl law upper bound [8] and meromorphic properties of dynamical zeta function [11].”