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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.
Rights: Tots els drets reservats.
Language: Anglès.
Document: article ; recerca ; submittedVersion
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 0022-247X

DOI: 10.1016/j.jmaa.2018.01.061


Preprint
23 p, 5.9 MB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2018-11-12, last modified 2019-02-02



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