On the connectivity of the Julia set of a finitely generated rational semigroup
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- by Yeshun Sun and Chung-Chun Yang PDF
- Proc. Amer. Math. Soc. 130 (2002), 49-52 Request permission
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.References
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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
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 49-52
- MSC (2000): Primary 37F10, 37F50
- DOI: https://doi.org/10.1090/S0002-9939-01-06097-X
- MathSciNet review: 1855618