On multiple recurrence and other properties of "nice" infinite measure preserving transformations

TL;DR

This paper explores advanced recurrence and mixing properties in infinite measure-preserving transformations, including Markov shifts and hyperbolic flows, highlighting their implications for multiple recurrence phenomena.

Contribution

It introduces multiple versions of rational ergodicity and weak mixing for a class of 'nice' transformations, extending understanding of recurrence in infinite measure systems.

Findings

Establishes multiple recurrence for these transformations

Connects rational ergodicity with weak mixing properties

Applies concepts to Markov shifts and hyperbolic flows

Abstract

We discuss multiple versions of rational ergodicity and rational weak mixing for "nice" transformations, including Markov shifts, certain interval maps and hyperbolic geodesic flows. These properties entail multiple recurrence.