Ruelle transfer operators for contact Anosov flows and decay of correlations

TL;DR

This paper demonstrates exponential decay of correlations for contact Anosov flows using spectral estimates of Ruelle transfer operators, applicable to Gibbs measures with specific Pesin set properties.

Contribution

It establishes strong spectral estimates for Ruelle transfer operators in contact Anosov flows, leading to decay of correlations results.

Findings

Exponential decay of correlations proven for Gibbs measures.

Spectral estimates for transfer operators are established.

Applicable to flows with Pesin sets with exponentially small tails.

Abstract

We prove exponential decay of correlations for H\"older continuous observables with respect to any Gibbs measure for contact Anosov flows admitting Pesin sets with exponentially small tails. This is achieved by establishing strong spectral estimates for certain Ruelle transfer operators for such flows.