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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On nearly abelian polynomial semigroups

Authors: Xiantao Wang and Zhigang Huang
Journal: Proc. Amer. Math. Soc. 133 (2005), 83-89
MSC (2000): Primary 30D05
Published electronically: August 10, 2004
MathSciNet review: 2085156
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Abstract: Let $G$ be a polynomial semigroup containing an element with degree at least 2 with the semigroup operation being functional composition. We prove that $G$ is nearly abelian if and only if the smallest $G-$completely invariant closed subset of the Riemann sphere is not equal to the Riemann sphere. We also give a positive answer to Conjecture 7.1 in Hinkkanen and Martin's paper on the dynamics of semigroups of rational functions.

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Additional Information

Xiantao Wang
Affiliation: Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, People’s Republic of China

Zhigang Huang
Affiliation: Department of Mathematics, Tsinghua University, Beijing 100080, People’s Repulic of China
Address at time of publication: Department of Mathematics, University of Science and Technology of SuZhou, Suzhou, Jiangsu 215011, People’s Republic of China

PII: S 0002-9939(04)07669-5
Keywords: Polynomial semigroup, nearly abelian, completely invariant, Green's function
Received by editor(s): August 15, 2003
Published electronically: August 10, 2004
Additional Notes: This research was partly supported by FNS of China (No. 10271043), Soft Project of Science and Technology of Hunan Province and the Foundation for Scholars back from Foreign Countries.
Communicated by: Linda Keen
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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