Homeomorphism groups of basilica, rabbit and airplane Julia sets
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910007938777088 |
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| author | Duchesne, Bruno Tarocchi, Matteo |
| author_facet | Duchesne, Bruno Tarocchi, Matteo |
| contents | The airplane, the basilica and the Douady rabbit (and, more generally, rabbits with more than two ears) are well-known Julia sets of complex quadratic polynomials.
In this paper we study the groups of all homeomorphisms of such fractals and of all automorphisms of their laminations.
In particular, we identify them with some kaleidoscopic group or universal groups and thus realize them as Polish permutation groups.
From these identifications, we deduce algebraic, topological and geometric properties of these groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homeomorphism groups of basilica, rabbit and airplane Julia sets Duchesne, Bruno Tarocchi, Matteo Dynamical Systems General Topology Group Theory The airplane, the basilica and the Douady rabbit (and, more generally, rabbits with more than two ears) are well-known Julia sets of complex quadratic polynomials. In this paper we study the groups of all homeomorphisms of such fractals and of all automorphisms of their laminations. In particular, we identify them with some kaleidoscopic group or universal groups and thus realize them as Polish permutation groups. From these identifications, we deduce algebraic, topological and geometric properties of these groups. |
| title | Homeomorphism groups of basilica, rabbit and airplane Julia sets |
| topic | Dynamical Systems General Topology Group Theory |
| url | https://arxiv.org/abs/2502.07762 |