Skew-product systems over infinite interval exchange transformations

TL;DR

This paper investigates the ergodic properties of skew-product systems over infinite interval exchange transformations, specifically rotated odometers, with applications to flows on infinite genus staircase manifolds.

Contribution

It introduces a new class of $ Z$-extensions called rotated odometers and analyzes their ergodic behavior, expanding understanding of infinite interval exchange transformations.

Findings

Analyzed recurrence and diffusion in rotated odometers.

Established ergodicity conditions for these systems.

Connected skew-product dynamics to flows on infinite genus surfaces.

Abstract

We study the ergodic properties (recurrence, discrepancy, diffusion coefficients and ergodicity itself) of a class of $\mathbb Z$-extensions over infinite interval exchange transformations called rotated odometers. The choice of a skew-function is motivated by the use in the study of parallel flows on a particular staircase manifold of infinite genus.