Home > Articles > Published articles > Rational maps with Fatou components of arbitrarily large connectivity |
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 ; 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 |
Postprint 23 p, 5.9 MB |