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arXiv · 2405.07645

Ergodicity of skew-products over typical IETs

Fernando Argentieri·Przemysław Berk·Frank Trujillo
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Abstract

We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \[ {T_f}:{[0, 1) \times \mathbb{R}}\to{[0, 1) \times \mathbb{R}},\quad {T_f(x, t)}:={(T(x), t+f(x))}, \] 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 ${Leb}_{[0,1)\times \mathbb{R}}$ for a typical choice of parameters of $T$ and $f$.

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Fernando Argentieri, Przemysław Berk, Frank Trujillo. 2024-05-13. Ergodicity of skew-products over typical IETs. https://arxiv.org/abs/2405.07645

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