Weak Mixing Property for Linear Involutions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917231675310080 |
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| author | Herrerías, Erick Gordillo |
| author_facet | Herrerías, Erick Gordillo |
| contents | In this work, we extend the celebrated result of Avila--Forni~\cite{avila2007weak} on the weak mixing property of interval exchange transformations to the setting of linear involutions, which naturally arise from the study of vertical foliations on half-translation surfaces. Using recent advances on the Kontsevich--Zorich cocycle for quadratic differentials~\cite{belldiagonal, gutierrez2019classification, trevino2013non}, we establish that, for every dynamically irreducible generalized permutation, the associated linear involution is weakly mixing for almost every admissible parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak Mixing Property for Linear Involutions Herrerías, Erick Gordillo Dynamical Systems In this work, we extend the celebrated result of Avila--Forni~\cite{avila2007weak} on the weak mixing property of interval exchange transformations to the setting of linear involutions, which naturally arise from the study of vertical foliations on half-translation surfaces. Using recent advances on the Kontsevich--Zorich cocycle for quadratic differentials~\cite{belldiagonal, gutierrez2019classification, trevino2013non}, we establish that, for every dynamically irreducible generalized permutation, the associated linear involution is weakly mixing for almost every admissible parameter. |
| title | Weak Mixing Property for Linear Involutions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2503.18909 |