Exponential mixing of all orders and CLT for generic birational maps of $\mathbb{P}^k$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910316244238336 |
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| author | De Thélin, Henry Vigny, Gabriel |
| author_facet | De Thélin, Henry Vigny, Gabriel |
| contents | For Hénon maps, Bianchi and Dinh recently proved the exponential mixing of all orders for the measure of maximal entropy and, as a consequence of the recent work of Björklund and Gorodnik, the CLT for Hölder observables.
We extend their results to generic birational maps of $\mathbb{P}^k$. Because of the indeterminacy set, Hölder maps are not stable under iteration, so we need to work with a suitable space of test functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponential mixing of all orders and CLT for generic birational maps of $\mathbb{P}^k$ De Thélin, Henry Vigny, Gabriel Dynamical Systems Complex Variables 37A25, 37A50, 37F80 For Hénon maps, Bianchi and Dinh recently proved the exponential mixing of all orders for the measure of maximal entropy and, as a consequence of the recent work of Björklund and Gorodnik, the CLT for Hölder observables. We extend their results to generic birational maps of $\mathbb{P}^k$. Because of the indeterminacy set, Hölder maps are not stable under iteration, so we need to work with a suitable space of test functions. |
| title | Exponential mixing of all orders and CLT for generic birational maps of $\mathbb{P}^k$ |
| topic | Dynamical Systems Complex Variables 37A25, 37A50, 37F80 |
| url | https://arxiv.org/abs/2402.01178 |