Ergodicity of skew-products over typical IETs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913424196239360 |
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| author | Argentieri, Fernando Berk, Przemysław Trujillo, Frank |
| author_facet | Argentieri, Fernando Berk, Przemysław Trujillo, Frank |
| contents | 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 $f$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_07645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ergodicity of skew-products over typical IETs Argentieri, Fernando Berk, Przemysław Trujillo, Frank Dynamical Systems 37E05, 37A40 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 $f$. |
| title | Ergodicity of skew-products over typical IETs |
| topic | Dynamical Systems 37E05, 37A40 |
| url | https://arxiv.org/abs/2405.07645 |