Some rigidity results for polynomial automorphisms of C^2
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929592625790976 |
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| author | Cantat, Serge Dujardin, Romain |
| author_facet | Cantat, Serge Dujardin, Romain |
| contents | We prove several new rigidity results for polynomial automorphisms of $\mathbb C^2$ with positive entropy. A first result is that a complex slice of the (forward or backward) Julia set is never a smooth, or even rectifiable, curve. We also show that such an automorphism cannot preserve a global holomorphic foliation, nor a real-analytic foliation with complex leaves.
These results are used to show that under mild assumptions, two real-analytically conjugate automorphisms are polynomially conjugate.
For mappings defined over a number field, we also study the fields of definition of multipliers of saddle periodic orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some rigidity results for polynomial automorphisms of C^2 Cantat, Serge Dujardin, Romain Dynamical Systems Complex Variables We prove several new rigidity results for polynomial automorphisms of $\mathbb C^2$ with positive entropy. A first result is that a complex slice of the (forward or backward) Julia set is never a smooth, or even rectifiable, curve. We also show that such an automorphism cannot preserve a global holomorphic foliation, nor a real-analytic foliation with complex leaves. These results are used to show that under mild assumptions, two real-analytically conjugate automorphisms are polynomially conjugate. For mappings defined over a number field, we also study the fields of definition of multipliers of saddle periodic orbits. |
| title | Some rigidity results for polynomial automorphisms of C^2 |
| topic | Dynamical Systems Complex Variables |
| url | https://arxiv.org/abs/2411.10339 |