Achievable connectivities of Fatou components for a family of singular perturbations
In this paper we study the connectivity of Fatou components for maps in a large family of singular perturbations. We prove that, for some parameters inside the family, the dynamical planes for the corresponding maps present Fatou components of arbitrarily large connectivity and we determine precisel...
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:267130 |
| Acesso em linha: | https://ddd.uab.cat/record/267130 https://dx.doi.org/urn:doi:10.3934/dcds.2022051 |
| Access Level: | acceso abierto |
| Palavra-chave: | Holomorphic dynamics Fatou and Julia sets Rational maps Singular perturbation Connectivity of Fatou components |
| Resumo: | In this paper we study the connectivity of Fatou components for maps in a large family of singular perturbations. We prove that, for some parameters inside the family, the dynamical planes for the corresponding maps present Fatou components of arbitrarily large connectivity and we determine precisely these connectivities. In particular, these results extend the ones obtained in [5, 6]. |
|---|