Achievable connectivities of Fatou components for a family of singular perturbations-Reference-Cited by-同舟云学术

Achievable connectivities of Fatou components for a family of singular perturbations

Published:2022 Issue:9 Volume:42 Page:4237
ISSN:1078-0947
Container-title:Discrete and Continuous Dynamical Systems
language:
Short-container-title:DCDS

Author:

Canela Jordi¹,Jarque Xavier²,Paraschiv Dan²

Affiliation:

1. Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, 12071 Castelló de la Plana, Spain

2. Departament de Matemàtiques i Informàtica at Universitat de Barcelona, and Barcelona Graduate School of Mathematics, 08007 Barcelona, Spain

Abstract

<p style='text-indent:20px;'>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 [<xref ref-type="bibr" rid="b5">5</xref>,<xref ref-type="bibr" rid="b6">6</xref>].</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

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