Ergodicity of skew-products over typical IETs

Fernando Argentieri, Przemysław Berk, Frank Trujillo

Published 2024-05-13Version 1

We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \[ \operatorname{T_f}{[0, 1) \times \mathbb{R}}{[0, 1) \times \mathbb{R}}{(x, t)}{(T(x), t+f(x))}, \] where $T$ is an interval exchange transformation and $f$ is a piece-wise constant function with a finite number of discontinuities. We show that such system is ergodic with respect to $\operatorname{Leb}_{[0,1)\times \mathbb{R}}$ for a typical choice of parameters of $T$ and $f$.