Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37F10, 37F50

Retrieve articles in all journals with MSC (2000): 37F10, 37F50


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: http://dx.doi.org/10.1090/S0002-9939-01-06097-X
PII: S 0002-9939(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