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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.04310 |
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| _version_ | 1866916755407896576 |
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| author | Xu, Disheng Zhang, Jiesong |
| author_facet | Xu, Disheng Zhang, Jiesong |
| contents | We construct examples illustrating that dynamically-defined distributions of holomorphic diffeomorphisms on compact complex manifolds are not necessarily holomorphic in any open subset. More precisely, for any $n\geq 5$, we construct a holomorphic fibered partially hyperbolic system on a complex $n$-fold, where the center distribution is not holomorphic in any open subset. For $n=3$ we demonstrate a contrast: the center distribution of any fibered holomorphic partially hyperbolic diffeomorphism on a complex $3$-fold is holomorphic. In particular, any such a system is a holomorphic skew product over a linear automorphism on a complex $2$-torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04310 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On holomorphic partially hyperbolic systems Xu, Disheng Zhang, Jiesong Dynamical Systems We construct examples illustrating that dynamically-defined distributions of holomorphic diffeomorphisms on compact complex manifolds are not necessarily holomorphic in any open subset. More precisely, for any $n\geq 5$, we construct a holomorphic fibered partially hyperbolic system on a complex $n$-fold, where the center distribution is not holomorphic in any open subset. For $n=3$ we demonstrate a contrast: the center distribution of any fibered holomorphic partially hyperbolic diffeomorphism on a complex $3$-fold is holomorphic. In particular, any such a system is a holomorphic skew product over a linear automorphism on a complex $2$-torus. |
| title | On holomorphic partially hyperbolic systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2401.04310 |