Rational Maps with Disconnected Julia Set
Abstract
We show that if f is a hyperbolic rational map with disconnected Julia set J, then with the possible exception of finitely many periodic components of J and their countable collection of preimages, every connected component of J is a point or a Jordan curve. As a corollary, every component of J is locally connected. We also discuss when a Jordan curve Julia component is a quasicircle and give an explicit example of a hyperbolic rational map with a Jordan curve Julia component which is not a quasicircle. © Astérisque 261, SMF 2000.
Recommended Citation
K. M. Pilgrim and T. Lei, "Rational Maps with Disconnected Julia Set," Asterisque, vol. 261, pp. 349 - 384, Société Mathematique de France, Dec 2000.
Department(s)
Mathematics and Statistics
Keywords and Phrases
Connected components; Iteration of rational maps; Jordan curve; Julia set
International Standard Serial Number (ISSN)
0303-1179
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Société Mathematique de France, All rights reserved.
Publication Date
01 Dec 2000
