Locating Ruelle-Pollicott resonances

TL;DR

This paper introduces a novel unitary approach to analyze the spectrum of transfer operators in various dynamical systems, providing detailed insights into Ruelle-Pollicott resonances across multiple settings.

Contribution

The paper proposes a new unitary method to precisely determine the discrete spectrum of transfer operators in diverse dynamical systems, including hyperbolic and expanding maps.

Findings

New insights into the spectrum of transfer operators for different dynamical systems.

A unified approach that can be generalized to various settings.

Potential for broad application in dynamical systems analysis.

Abstract

We study the spectrum of transfer operators associated to various dynamical systems. Our aim is to obtain precise information on the discrete spectrum. To this end we propose a unitary approach. We consider various settings where new information can be obtained following different branches along the proposed path. These settings include affine expanding Markov maps, uniformly expanding Markov maps, non-uniformly expanding or simply monotone maps, hyperbolic diffeomorphisms. We believe this approach could be greatly generalized.