Polynomial decay of correlations for nonpositively curved surfaces

TL;DR

This paper proves polynomial decay of correlations and establishes statistical limit laws like the central limit theorem for geodesic flows on certain nonpositively curved surfaces with specific curvature conditions.

Contribution

It introduces new results on decay rates and statistical properties for geodesic flows on nonpositively curved surfaces with zero curvature along a single closed geodesic.

Findings

Polynomial decay of correlations established

Statistical limit laws proven for the flows

Applicable to surfaces with specific curvature conditions

Abstract

We prove polynomial decay of correlations for geodesic flows on a class of nonpositively curved surfaces where zero curvature only occurs along one closed geodesic. We also prove that various statistical limit laws, including the central limit theorem, are satisfied by this class of geodesic flows.