Sharp polynomial bounds on the number of Pollicott-Ruelle resonances
Spectral Theory
2019-02-20 v4 Analysis of PDEs
Dynamical Systems
Abstract
We give a sharp polynomial bound on the number of Pollicott-Ruelle resonances. These resonances, which are complex numbers in the lower half-plane, appear in expansions of correlations for Anosov contact flows. The bounds follow the tradition of upper bounds on the number of scattering resonances and improve a recent bound of Faure-Sj\"ostrand. The complex scaling method used in scattering theory is replaced by an approach using exponentially weighted spaces introduced by Helffer-Sj\"ostrand in scattering theory and by Faure-Sj\"ostrand in the theory of Anosov flows.
Keywords
Cite
@article{arxiv.1208.4330,
title = {Sharp polynomial bounds on the number of Pollicott-Ruelle resonances},
author = {Kiril Datchev and Semyon Dyatlov and Maciej Zworski},
journal= {arXiv preprint arXiv:1208.4330},
year = {2019}
}
Comments
18 pages; minor revision based on referee's comments. To appear in Erg. Theory Dyn. Syst