Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances

TL;DR

This paper applies semi-classical analysis to study spectral properties of Anosov diffeomorphisms, specifically Ruelle resonances, linking dynamical systems with quantum resonance theories.

Contribution

It introduces a novel semi-classical framework to analyze Ruelle resonances of Anosov diffeomorphisms using quantum resonance techniques.

Findings

Ruelle resonances can be interpreted as quantum resonances.

Spectral properties of Anosov diffeomorphisms are accessible via semi-classical methods.

The approach bridges dynamical systems and quantum resonance theories.

Abstract

In this paper, we show that some spectral properties of Anosov diffeomorphisms can be obtained by semi-classical analysis. In particular the Ruelle resonances which are eigenvalues of the Ruelle transfer operator acting in suitable anisotropic Sobolev spaces and which govern the decay of dynamical correlations, can be treated as the quantum resonances of open quantum systems in the Aguilar-Baslev-Combes theory or the more recent Helffer-Sjostrand phase-space theory.