On nearly abelian polynomial semigroups
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- by Xiantao Wang and Zhigang Huang PDF
- Proc. Amer. Math. Soc. 133 (2005), 83-89 Request permission
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.References
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Additional Information
- Xiantao Wang
- Affiliation: Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, People’s Republic of China
- Email: xtwang@mail.hunnu.edu.cn
- 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
- Email: huang.z.g@263.sina.com
- 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
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 83-89
- MSC (2000): Primary 30D05
- DOI: https://doi.org/10.1090/S0002-9939-04-07669-5
- MathSciNet review: 2085156