Ergodicity of skew products over linearly recurrent IETs

TL;DR

This paper proves that certain skew products over linearly recurrent interval exchange transformations are ergodic with respect to Lebesgue measure, for a broad class of real-valued functions.

Contribution

It establishes ergodicity for skew products over linearly recurrent IETs for almost any mean-zero linear combination of interval characteristic functions.

Findings

Ergodicity holds for almost all such functions.

The result applies to a broad class of linear combinations.

It advances understanding of dynamical properties of IETs.

Abstract

We prove that the skew product over a linearly recurrent interval exchange transformation defined by almost any real-valued, mean-zero linear combination of characteristic functions of intervals is ergodic with respect to Lebesgue measure.