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Density of hyperbolicity for rational maps with Cantor Julia sets

Published online by Cambridge University Press:  08 September 2011

WENJUAN PENG ,
YONGCHENG YIN  and
YU ZHAI
WENJUAN PENG
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, PR China (email: [email protected])
YONGCHENG YIN
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, 310027, PR China (email: [email protected])
YU ZHAI
Affiliation:
Department of Mathematics, School of Science, China University of Mining and Technology (Beijing), Beijing 100083, PR China (email: [email protected])
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Abstract

In this paper, taking advantage of quasi-conformal surgery, we prove that each non-hyperbolic rational map with a Cantor Julia set can be approximated by hyperbolic rational maps with Cantor Julia sets of the same degree.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 5 , October 2012 , pp. 1711 - 1726
Copyright
Copyright © Cambridge University Press 2011

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