Achievable connectivities of Fatou components for a family of singular perturbations
Canela Sánchez, Jordi (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló)
Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Paraschiv, Dan (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)

Date:	2022
Abstract:	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].
Grants:	Ministerio de Economía y Competitividad MDM-2014-0445 Agencia Estatal de Investigación MTM-2017-86795-C3-2-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1374
Note:	Altres ajuts: BGSMath Banco de Santander Postdoctoral 2017, the project UJI-B2019-18 from Universitat Jaume I and Spanish government grant FPI PRE2018-086831
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Holomorphic dynamics ; Fatou and Julia sets ; Rational maps ; Singular perturbation ; Connectivity of Fatou components
Published in:	Discrete and continuous dynamical systems. Series A, Vol. 42, Issue 9 (September 2022) , p. 4237-4261, ISSN 1553-5231

DOI: 10.3934/dcds.2022051

Postprint 25 p, 1.5 MB

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