Ergodicity of certain cocycles over certain interval exchanges

TL;DR

This paper proves that for a specific class of interval exchange transformations with odd-valued piecewise-constant cocycles, the associated skew products are ergodic for almost all parameter choices.

Contribution

It establishes ergodicity results for a new class of skew products over interval exchanges with odd-valued cocycles, expanding understanding of their dynamical behavior.

Findings

Ergodicity holds for full-measure parameter sets.

Results apply to a specific two-parameter family of interval exchanges.

The paper advances the theory of cocycles over interval exchanges.

Abstract

We show that for odd-valued piecewise-constant skew products over a certain two parameter family of interval exchanges, the skew product is ergodic for a full-measure choice of parameters.