Beau bounds for multicritical circle maps |
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| Authors: | Gabriela Estevez Edson de Faria Pablo Guarino |
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| Affiliation: | 1. Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 31270-901, Belo Horizonte MG, Brazil;2. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090, São Paulo SP, Brazil;3. Instituto de Matemática e Estatística, Universidade Federal Fluminense, Rua Prof. Marcos Waldemar de Freitas Reis, S/N, 24.210-201, Bloco H, Campus do Gragoatá, São Domingos, Niterói, Rio de Janeiro, Brazil |
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| Abstract: | Let be a homeomorphism without periodic points having a finite number of critical points of power-law type. In this paper we establish real a-priori bounds, on the geometry of orbits of , which are beau in the sense of Sullivan, i.e. bounds that are asymptotically universal at small scales. The proof of the beau bounds presented here is an adaptation, to the multicritical setting, of the one given by the second author and de Melo in de Faria and de Melo (1999), for the case of a single critical point. |
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| Keywords: | Real bounds Multicritical circle maps Quasisymmetric rigidity Dynamical partitions |
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