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On the connectivity of the Julia set of a finitely generated rational semigroup


Authors: Yeshun Sun and Chung-Chun Yang
Journal: Proc. Amer. Math. Soc. 130 (2002), 49-52
MSC (2000): Primary 37F10, 37F50
Published electronically: May 3, 2001
MathSciNet review: 1855618
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Abstract | References | Similar Articles | Additional Information

Abstract:

In this paper we show that the Julia set $J(G)$ of a finitely generated rational semigroup $G$ is connected if the union of the Julia sets of generators is contained in a subcontinuum of $J(G)$. Under a nonseparating condition, we prove that the Julia set of a finitely generated polynomial semigroup is connected if its postcritical set is bounded.


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Additional Information

Yeshun Sun
Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
Address at time of publication: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, Peoples’ Republic of China
Email: maysun@ust.hk, sun@math.zju.edu.cn

Chung-Chun Yang
Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
Email: mayang@ust.hk

DOI: https://doi.org/10.1090/S0002-9939-01-06097-X
Keywords: Connectivity, Julia set, rational semigroup
Received by editor(s): May 4, 2000
Published electronically: May 3, 2001
Additional Notes: This research was partially supported by a UGC grant of Hong Kong, Project No. 6070/98P
Communicated by: Linda Keen
Article copyright: © Copyright 2001 American Mathematical Society