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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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  • J. Milnor, Dynamics in one complex variable: Introductory lectures, Vieweg Verlag, 1999.
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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