Stochastic stability of Pollicott-Ruelle resonances
Dynamical Systems
2016-09-22 v2 Analysis of PDEs
Spectral Theory
Abstract
Pollicott-Ruelle resonances for chaotic flows are the characteristic frequencies of correlations. They are typically defined as eigenvalues of the generator of the flow acting on specially designed functional spaces. We show that these resonances can be computed as viscosity limits of eigenvalues of second order elliptic operators. These eigenvalues are the characteristic frequencies of correlations for a stochastically perturbed flow.
Keywords
Cite
@article{arxiv.1407.8531,
title = {Stochastic stability of Pollicott-Ruelle resonances},
author = {Semyon Dyatlov and Maciej Zworski},
journal= {arXiv preprint arXiv:1407.8531},
year = {2016}
}
Comments
26 pages, 6 figures. Added several negative examples at the end of the introduction