Decay of correlations on Abelian covers of isometric extensions of volume-preserving Anosov flows

TL;DR

This paper proves an asymptotic expansion for the correlation function of isometric extensions of volume-preserving Anosov flows on Abelian covers, advancing understanding of their long-term statistical behavior.

Contribution

It introduces a novel asymptotic expansion in inverse powers of time for correlations in Abelian covers of Anosov flows, extending previous results to a broader class of dynamical systems.

Findings

Established asymptotic expansion of correlation functions

Extended analysis to Abelian covers of Anosov flows

Provided new insights into long-term statistical properties

Abstract

We establish an asymptotic expansion in inverse powers of time of the correlation function of isometric extensions of volume-preserving Anosov flows on Abelian covers of closed manifolds.