Rational maps with Fatou components of arbitrarily large connectivity
We study the family of singular perturbations of Blaschke products B_a,(z)=z^3-a1- ^2. We analyse how the connectivity of the Fatou components varies as we move continuously the parameter . We prove that all possible escaping configurations of the critical point c_-(a,) take place within the paramet...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:199372 |
| Acceso en línea: | https://ddd.uab.cat/record/199372 https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.01.061 |
| Access Level: | acceso abierto |
| Palabra clave: | Holomorphic dynamics Blaschke products McMullen-like Julia sets Singular perturbations Connectivity of Fatou components |
| Sumario: | We study the family of singular perturbations of Blaschke products B_a,(z)=z^3-a1- ^2. We analyse how the connectivity of the Fatou components varies as we move continuously the parameter . We prove that all possible escaping configurations of the critical point c_-(a,) take place within the parameter space. In particular, we prove that there are maps B_a, which have Fatou components of arbitrarily large finite connectivity within their dynamical planes. |
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