Topology of irrationally indifferent attractors
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arXiv
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866912377841123328 |
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| author | Cheraghi, Davoud |
| author_facet | Cheraghi, Davoud |
| contents | We study the post-critical set of a class of holomorphic systems with an irrationally indifferent fixed point. We prove a trichotomy for the topology of the post-critical set based on the arithmetic of the rotation number at the fixed point. The only options are Jordan curves, a one-sided hairy Jordan curves, and Cantor bouquet. This explains the degeneration of the closed invariant curves inside the Siegel disks, as one varies the rotation number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_02678 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Topology of irrationally indifferent attractors Cheraghi, Davoud Dynamical Systems Functional Analysis Number Theory 37F50 (Primary), 37F10, 46T25 (Secondary) We study the post-critical set of a class of holomorphic systems with an irrationally indifferent fixed point. We prove a trichotomy for the topology of the post-critical set based on the arithmetic of the rotation number at the fixed point. The only options are Jordan curves, a one-sided hairy Jordan curves, and Cantor bouquet. This explains the degeneration of the closed invariant curves inside the Siegel disks, as one varies the rotation number. |
| title | Topology of irrationally indifferent attractors |
| topic | Dynamical Systems Functional Analysis Number Theory 37F50 (Primary), 37F10, 46T25 (Secondary) |
| url | https://arxiv.org/abs/1706.02678 |