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Bull. Korean Math. Soc. 2013; 50(1): 343-351

Printed January 31, 2013

https://doi.org/10.4134/BKMS.2013.50.1.343

Copyright © The Korean Mathematical Society.

Singularities and strictly wandering domains of transcendental semigroups

Zhi Gang Huang and Tao Cheng

Suzhou University of Science and Technology, East China Normal University

Abstract

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In this paper, the dynamics on a transcendental entire semigroup $G$ is investigated. We show the possible values of any limit function of $G$ in strictly wandering domains and Fatou components, respectively. Moreover, if $G$ is of class $\mathfrak{B}$, for any $z$ in a Fatou domain, there does not exist a sequence $\{g_k\}$ of $G$ such that $g_k(z)\rightarrow\infty$ as $k\rightarrow\infty$.

Keywords: transcendental semigroup, strictly wandering domain, limit function, singularity

MSC numbers: 37F10, 30D05

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