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On nearly abelian polynomial semigroups |
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| Authors: | Xiantao Wang Zhigang Huang |
| Institution: | Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, People's Republic of China ; Department of Mathematics, Tsinghua University, Beijing 100080, People's Repulic of China |
| Abstract: | Let  be a polynomial semigroup containing an element with degree at least 2 with the semigroup operation being functional composition. We prove that  is nearly abelian if and only if the smallest  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. |
| Keywords: | Polynomial semigroup nearly abelian completely invariant Green's function |
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