On the rate of mixing of circle extensions of Anosov maps

TL;DR

This paper investigates the mixing rates of circle extensions of Anosov maps on the torus, providing explicit lower bounds related to topological pressure, especially for random trigonometric polynomial extensions.

Contribution

It offers new explicit lower bounds on mixing rates for partially hyperbolic circle extensions of Anosov maps, including cases with random trigonometric polynomial roof functions.

Findings

Derived explicit lower bounds involving topological pressure.

Analyzed mixing rates for random trigonometric polynomial extensions.

Enhanced understanding of ergodic properties of partially hyperbolic maps.

Abstract

We study circle extensions of analytic Anosov maps on the two torus: these are examples of partially hyperbolic maps for which the qualitative ergodic theory is well understood. In this paper we investigate rates of mixing (for the SRB measure) and prove explicit lower bounds involving the topological pressure of two times the unstable Jacobian. In particular we study the case when the extension function ("roof function") is given by a random trigonometric polynomial.