The high type quadratic Siegel disks are Jordan domains
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866911845992890368 |
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| author | Shishikura, Mitsuhiro Yang, Fei |
| author_facet | Shishikura, Mitsuhiro Yang, Fei |
| contents | Let $α$ be an irrational number of sufficiently high type and suppose $P_α(z)=e^{2πiα}z+z^2$ has a Siegel disk $Δ_α$ centered at the origin. We prove that the boundary of $Δ_α$ is a Jordan curve, and that it contains the critical point $-e^{2πiα}/2$ if and only if $α$ is a Herman number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1608_04106 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | The high type quadratic Siegel disks are Jordan domains Shishikura, Mitsuhiro Yang, Fei Dynamical Systems Primary 37F10, Secondary 37F50 Let $α$ be an irrational number of sufficiently high type and suppose $P_α(z)=e^{2πiα}z+z^2$ has a Siegel disk $Δ_α$ centered at the origin. We prove that the boundary of $Δ_α$ is a Jordan curve, and that it contains the critical point $-e^{2πiα}/2$ if and only if $α$ is a Herman number. |
| title | The high type quadratic Siegel disks are Jordan domains |
| topic | Dynamical Systems Primary 37F10, Secondary 37F50 |
| url | https://arxiv.org/abs/1608.04106 |