Dynamics of Schwarz reflections: the mating phenomena
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866908352121929728 |
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| author | Lee, Seung-Yeop Lyubich, Mikhail Makarov, Nikolai G. Mukherjee, Sabyasachi |
| author_facet | Lee, Seung-Yeop Lyubich, Mikhail Makarov, Nikolai G. Mukherjee, Sabyasachi |
| contents | We initiate the exploration of a new class of anti-holomorphic dynamical systems generated by Schwarz reflection maps associated with quadrature domains. More precisely, we study Schwarz reflection with respect to the deltoid, and Schwarz reflections with respect to the cardioid and a family of circumscribing circles. We describe the dynamical planes of the maps in question, and show that in many cases, they arise as unique conformal matings of quadratic anti-holomorphic polynomials and the ideal triangle group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_04979 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Dynamics of Schwarz reflections: the mating phenomena Lee, Seung-Yeop Lyubich, Mikhail Makarov, Nikolai G. Mukherjee, Sabyasachi Dynamical Systems Complex Variables 37F10, 37F30, 30D05, 30C45, 76D27, 82B21 We initiate the exploration of a new class of anti-holomorphic dynamical systems generated by Schwarz reflection maps associated with quadrature domains. More precisely, we study Schwarz reflection with respect to the deltoid, and Schwarz reflections with respect to the cardioid and a family of circumscribing circles. We describe the dynamical planes of the maps in question, and show that in many cases, they arise as unique conformal matings of quadratic anti-holomorphic polynomials and the ideal triangle group. |
| title | Dynamics of Schwarz reflections: the mating phenomena |
| topic | Dynamical Systems Complex Variables 37F10, 37F30, 30D05, 30C45, 76D27, 82B21 |
| url | https://arxiv.org/abs/1811.04979 |