Paper Fortune Tellers in the combinatorial dynamics of some generalized McMullen maps with both critical orbits bounded
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917891566206976 |
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| author | Boyd, Suzanne Brouwer, Kelsey |
| author_facet | Boyd, Suzanne Brouwer, Kelsey |
| contents | For the family of complex rational functions known as "Generalized McMullen maps", F(z) = z^n + a/z^n+b, for complex parameters a and b, with a nonzero, and any integer n at least 3 fixed, we reveal, and provide a combinatorial model for, some new dynamical behavior. In particular, we describe a large class of maps whose Julia sets contain both infinitely many homeomorphic copies of quadratic Julia sets and infinitely many subsets homeomorphic to a set which is obtained by starting with a quadratic Julia set, then changing a finite number of pairs of external ray landing point identifications, following an algorithm we will describe. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Paper Fortune Tellers in the combinatorial dynamics of some generalized McMullen maps with both critical orbits bounded Boyd, Suzanne Brouwer, Kelsey Dynamical Systems 37F10 (Primay) 37F12, 37F20 (Secondary) For the family of complex rational functions known as "Generalized McMullen maps", F(z) = z^n + a/z^n+b, for complex parameters a and b, with a nonzero, and any integer n at least 3 fixed, we reveal, and provide a combinatorial model for, some new dynamical behavior. In particular, we describe a large class of maps whose Julia sets contain both infinitely many homeomorphic copies of quadratic Julia sets and infinitely many subsets homeomorphic to a set which is obtained by starting with a quadratic Julia set, then changing a finite number of pairs of external ray landing point identifications, following an algorithm we will describe. |
| title | Paper Fortune Tellers in the combinatorial dynamics of some generalized McMullen maps with both critical orbits bounded |
| topic | Dynamical Systems 37F10 (Primay) 37F12, 37F20 (Secondary) |
| url | https://arxiv.org/abs/2501.07545 |