Stochastic stability of Pollicott-Ruelle resonances

TL;DR

This paper demonstrates that Pollicott-Ruelle resonances, which characterize chaotic flow correlations, can be obtained as viscosity limits of eigenvalues of elliptic operators associated with stochastically perturbed flows.

Contribution

It introduces a novel method to compute Pollicott-Ruelle resonances via viscosity limits of elliptic operator eigenvalues, linking deterministic and stochastic flow analysis.

Findings

Resonances are the eigenvalues of flow generators on specialized spaces.

Resonances can be approximated by eigenvalues of elliptic operators with viscosity.

Stochastic perturbations provide a new computational approach for these 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.