Rational maps with Fatou components of arbitrarily large connectivity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Canela, Jordi¹ 

[1] Univ Paul Sabatier, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse, France

关键词: Holornorphic dynamics;    Blaschke products;    McMullen-like Julia sets;    Singular perturbations;    Connectivity of Fatou components;   

DOI  :  10.1016/j.jmaa.2018.01.061

来源: Elsevier

【 摘 要 】

We study the family of singular perturbations of Blaschke products B-alpha,B- lambda(z) = z(3) z-a/1-az + lambda/z(2).We analyse how the connectivity of the Fatou components varies as we move continuously the parameter lambda. We prove that all possible escaping configurations of the critical point c-(a, lambda) take place within the parameter space. In particular, we prove that there are maps B alpha, lambda which have Fatou components of arbitrarily large finite connectivity within their dynamical planes. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free