Rational maps with Fatou components of arbitrarily large connectivity
Canela Sánchez, Jordi (Université Paul Sabatier. Institut de Mathématiques de Toulouse)

Date:	2018
Abstract:	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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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Holomorphic dynamics ; Blaschke products ; McMullen-like Julia sets ; Singular perturbations ; Connectivity of Fatou components
Published in:	Journal of mathematical analysis and applications, Vol. 462, issue 1 (June 2018) , p. 35-56, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2018.01.061

Postprint 23 p, 5.9 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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