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http://dx.doi.org/10.4134/BKMS.2013.50.1.343

SINGULARITIES AND STRICTLY WANDERING DOMAINS OF TRANSCENDENTAL SEMIGROUPS  

Huang, Zhi Gang (Department of Mathematics Suzhou University of Science and Technology)
Cheng, Tao (Department of Mathematics Suzhou University of Science and Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.1, 2013 , pp. 343-351 More about this Journal
Abstract
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;
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1 I. N. Baker, Limit functions and sets of non-normality in iteration theory, Ann. Acad. Sci. Fenn. Ser. A I. 467 (1970), 2-11.
2 I. N. Baker, Wandering domains in the iteration of entire functions, Proc. London Math. Soc. (3) 49 (1984), no. 3, 563-576.
3 I. N. Baker, Limit functions in wandering domains of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 27 (2002), no. 2, 499-505.
4 W. Bergweiler, Iteration of meromorphic functions, Bull. Amer. Math. Soc. 29 (1993), no. 2, 151-188.   DOI
5 W. Bergweiler, M. Haruke, H. Kriete, H. G. Meier, and N. Terglane, On the limit functions of iterates in wandering domains, Ann. Acad. Sci. Fenn. Ser. A I Math. 18 (1993), no. 2, 369-375.
6 W. Bergweiler and Y. F. Wang, On the dynamics of composite entire functions, Ark. Mat. 36 (1998), no. 1, 31-39.   DOI
7 A. E. Eremenko and M. Y. Lyubich, Dynamical properties of some classes of entire functions, Ann. Inst. Fourier (Grenoble) 42 (1992), no. 4, 989-1020.   DOI
8 A. Hinkkanen and G. J. Martin, The dynamics of semigroups of rational functions. I, Proc. London Math. Soc. (3) 73 (1996), no. 2, 358-384.
9 A. Hinkkanen and G. J. Martin, Julia sets of rational semigroups, Math. Z. 222 (1996), no. 2, 161-169.   DOI
10 M. R. Perez, Sur une question de Dulac et Fatou, C. R. Acad. Sci. Paris Ser. I Math. 321 (1995), no. 8, 1045-1048.
11 K. K. Poon, Fatou-Julia theory on transcendental semigroups, Bull. Austral. Math. Soc. 58 (1998), no. 3, 403-410.   DOI
12 K. K. Poon, Fatou-Julia theory on transcendental semigroups. II, Bull. Austral. Math. Soc. 59 (1999), no. 2, 257-262.   DOI
13 D. Sullivan, Quasiconformal homeomorphisms and dynamics I: Solution of the Fatou-Julia problem on wandering domains, Ann. of Math. (2) 122 (1985), no. 3, 401-418.   DOI
14 J. H. Zheng, On transcendental meromorphic functions which are geometrically finite, J. Aust. Math. Soc. 72 (2002), no. 1, 93-107.   DOI
15 J. H. Zheng, Singularities and wandering domains in iteration of meromorphic functions, Illinois J. Math. 44 (2000), no. 3, 520-530.
16 J. H. Zheng, Singularities and limit functions in iteration of meromorphic functions, J. London Math. Soc. (2) 67 (2003), no. 1, 195-207.   DOI
17 J. H. Zheng, Iteration of functions which are meromorphic outside a small set, Tohoku Math. J. (2) 57 (2005), no. 1, 23-43.   DOI