Regular variation and rates of mixing for infinite measure preserving almost Anosov diffeomorphisms

TL;DR

This paper investigates the mixing rates of infinite measure preserving almost Anosov diffeomorphisms on the 2D torus by analyzing the regular variation of tail distributions of first return times near neutral fixed points.

Contribution

It establishes the regular variation of tail distributions for first return times, providing new insights into the mixing behavior of these dynamical systems.

Findings

Proves regular variation of tail distributions near neutral fixed points

Derives mixing rates for infinite measure preserving almost Anosov diffeomorphisms

Enhances understanding of statistical properties of such systems

Abstract

The purpose of this paper is to establish mixing rates for infinite measure preserving almost Anosov diffeomorphisms on the two-dimensional torus. The main task is to establish regular variation of the tails of the first return time to the complement of a neighbourhood of the neutral fixed point.