Unique ergodicity for singular holomorphic foliations of $\mathbb{P}^3(\mathbb{C})$ with an invariant plane
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916568909217792 |
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| author | Lequen, Félix |
| author_facet | Lequen, Félix |
| contents | We prove a unique ergodicity theorem for singular holomorphic foliations of $\mathbb{P}^3(\mathbb{C})$ with hyperbolic singularities and with an invariant plane with no foliation cycle, in analogy with a result of Dinh-Sibony concerning unique ergodicity for foliations of $\mathbb{P}^2(\mathbb{C})$ with an invariant line. The proof is dynamical in nature and adapts the work of Deroin-Kleptsyn to a singular context, using the fundamental integrability estimate of Nguyên. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01531 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Unique ergodicity for singular holomorphic foliations of $\mathbb{P}^3(\mathbb{C})$ with an invariant plane Lequen, Félix Dynamical Systems Complex Variables We prove a unique ergodicity theorem for singular holomorphic foliations of $\mathbb{P}^3(\mathbb{C})$ with hyperbolic singularities and with an invariant plane with no foliation cycle, in analogy with a result of Dinh-Sibony concerning unique ergodicity for foliations of $\mathbb{P}^2(\mathbb{C})$ with an invariant line. The proof is dynamical in nature and adapts the work of Deroin-Kleptsyn to a singular context, using the fundamental integrability estimate of Nguyên. |
| title | Unique ergodicity for singular holomorphic foliations of $\mathbb{P}^3(\mathbb{C})$ with an invariant plane |
| topic | Dynamical Systems Complex Variables |
| url | https://arxiv.org/abs/2212.01531 |