Stochastic stability of Pollicott-Ruelle resonances

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.

26 pages, 6 figures. Added several negative examples at the end of the introduction

References in corpus (3)

• Power spectrum of the geodesic flow on hyperbolic manifolds
• Leading Pollicott-Ruelle Resonances and Transport in Area-Preserving Maps
• On the spectra of quenched random perturbations of partially expanding maps on the torus

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• Resonances as viscosity limits for black box perturbations
• Kolmogorov Modes and Linear Response of Jump-Diffusion Models
• Complex absorbing potential method for Stark resonances