Pollicott-Ruelle resolvent and Sobolev regularity

TL;DR

This paper determines the minimal Sobolev regularity required for the meromorphic continuation of the Pollicott-Ruelle resolvent of Anosov flows, linking it to decay of correlations in dynamical systems.

Contribution

It extends the analysis of the Pollicott-Ruelle resolvent to general vector bundles and identifies the threshold Sobolev regularity for meromorphic continuation.

Findings

Threshold regularity for meromorphic continuation computed.

Relation established between regularity and decay of correlations.

Results applicable to general vector bundles.

Abstract

In this note we compute the threshold regularity for meromorphic continuation of the Pollicott--Ruelle resolvent of an Anosov flow as an operator on anisotropic Sobolev spaces, in the setting of lifts to general vector bundles. These thresholds are related to the Sobolev regularity needed for the decay of correlations.