Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.01868 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917629996826624 |
|---|---|
| author | Berk, Przemysław Trujillo, Frank |
| author_facet | Berk, Przemysław Trujillo, Frank |
| contents | In this article, we consider skew product extensions over symmetric interval exchange transformations with respect to the cocycle $f(x)=χ_{(0,1/2)}-χ_{(1/2,1)}$. More precisely, we prove that for almost every interval exchange transformation $T$ with symmetric combinatorial data, the skew product $T_f: [0, 1) \times \mathbb Z \to [0, 1) \times \mathbb Z$ given by $T_f(x,r)=(T(x),r+f(x))$ is ergodic with respect to the product of the Lebesgue and counting measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01868 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the ergodicity of infinite antisymmetric extensions of symmetric IETs Berk, Przemysław Trujillo, Frank Dynamical Systems In this article, we consider skew product extensions over symmetric interval exchange transformations with respect to the cocycle $f(x)=χ_{(0,1/2)}-χ_{(1/2,1)}$. More precisely, we prove that for almost every interval exchange transformation $T$ with symmetric combinatorial data, the skew product $T_f: [0, 1) \times \mathbb Z \to [0, 1) \times \mathbb Z$ given by $T_f(x,r)=(T(x),r+f(x))$ is ergodic with respect to the product of the Lebesgue and counting measure. |
| title | On the ergodicity of infinite antisymmetric extensions of symmetric IETs |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2304.01868 |