A hybrid method for calculation of Ruelle-Pollicott resonances

TL;DR

This paper introduces a numerical hybrid method to compute Ruelle-Pollicott resonances in dynamical systems, improving efficiency and robustness over traditional approaches by using coarse-grained propagators based on multiple observables and time steps.

Contribution

The paper presents a novel hybrid numerical approach for calculating Ruelle-Pollicott resonances that enhances efficiency and robustness compared to existing methods.

Findings

Method is numerically efficient

Method is robust against perturbations

Validated on perturbed cat map

Abstract

We present a numerical method for calculation of Ruelle-Pollicott resonances of dynamical systems. It constructs an effective coarse-grained propagator by considering the correlations of multiple observables over multiple timesteps. The method is compared to the usual approaches on the example of the perturbed cat map and is shown to be numerically efficient and robust.