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...

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Detalhes bibliográficos
Autores: Canela Sánchez, Jordi|||0000-0001-7879-5438, Jarque i Ribera, Xavier|||0000-0002-6576-9780, Paraschiv, Dan
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
Descrição
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].