Rigidity of bounded type cubic Siegel polynomials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910549582807040 |
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| author | Yang, Jonguk Zhang, Runze |
| author_facet | Yang, Jonguk Zhang, Runze |
| contents | We prove that if two non-renormalizable cubic Siegel polynomials with bounded type rotation numbers are combinatorially equivalent, then they are also conformally equivalent. As a consequence, we show that in the one-parameter slice of cubic Siegel polynomials considered by Zakeri [Za2], the locus of non-renormalizable maps is homeomorphic to a double-copy of a quadratic Siegel filled Julia set (minus the Siegel disk) glued along the Siegel boundary. This verifies the the conjecture of Blokh-Oversteegen-Ptacek-Timorin [BlOvPtTi] for bounded type rotation numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00431 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity of bounded type cubic Siegel polynomials Yang, Jonguk Zhang, Runze Dynamical Systems We prove that if two non-renormalizable cubic Siegel polynomials with bounded type rotation numbers are combinatorially equivalent, then they are also conformally equivalent. As a consequence, we show that in the one-parameter slice of cubic Siegel polynomials considered by Zakeri [Za2], the locus of non-renormalizable maps is homeomorphic to a double-copy of a quadratic Siegel filled Julia set (minus the Siegel disk) glued along the Siegel boundary. This verifies the the conjecture of Blokh-Oversteegen-Ptacek-Timorin [BlOvPtTi] for bounded type rotation numbers. |
| title | Rigidity of bounded type cubic Siegel polynomials |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2311.00431 |