Heat kernel and the rate of mixing for compact extensions of expanding maps

TL;DR

This paper investigates how skew extensions of expanding maps by compact Lie groups mix over time, providing explicit bounds on the rate of exponential mixing using advanced mathematical tools.

Contribution

It introduces a new lower bound on the mixing rate for these systems, combining representation theory and PDE estimates.

Findings

Established explicit lower bounds on exponential mixing rates.

Connected mixing properties with topological pressure.

Applied representation theory and elliptic PDE techniques.

Abstract

We consider skew extensions of expanding maps by compact Lie groups. For a class of natural invariant measures, we prove an explicit lower bound on the rate of (exponential) mixing involving topological pressure. Proof uses representation theory and some elliptic pde estimates.