On the growth of transcendental entire functions with multiply. (English) Zbl 1140.37339
Summary: Let \(g\) and \(h\) be two transcendental entire functions. Suppose that the Fatou set \(F(g\circ h)\) contains multiply connected components. The authors consider the growth of the functions \(g\) and \(h\).
MSC:
| 37F10 | Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets |
| 37F50 | Small divisors, rotation domains and linearization in holomorphic dynamics |
References:
| [1] | Hua Xin-hou, Yang Chung-chun. Dynamics of Transcendental Functions[M]. Amsterdam: Gordon and Breach Science Publishers, 1998. · Zbl 0934.30021 |
| [2] | Morosawa S, Nishimura Y, Taniguchi M, Ueda T. Holomorphic Dynamics [M]. London: Cambridge University Press, 2000. |
| [3] | Bergweiler W. Iteration of meromorphic functions[J]. Bulletin of the American Mathematical Society, 1993, 29(2): 151–188. · Zbl 0791.30018 · doi:10.1090/S0273-0979-1993-00432-4 |
| [4] | Baker I N. Some entire functions with multiply connected wandering domains[J]. Ergodic Theory and Dynamical Systems, 1985, 5: 163–169. · doi:10.1017/S0143385700002832 |
| [5] | Cao Chun-lei, Wang Yue-fei. On the simple connectivity of Fatou components[J]. Acta Mathematica Sinica, 2002, 18(4): 625–630. · Zbl 1027.37028 · doi:10.1007/s10114-002-0217-3 |
| [6] | Wang Xiao-ling, Yang Chung-chun. On the wandering and Baker domains of transcendental entire functions[J]. International Journal of Bifurcation and Chaos, 2004, 14(1): 321–327. · Zbl 1101.37035 · doi:10.1142/S021812740400903X |
| [7] | Zheng Jian-hua. On multiply-connected Fatou components in iteration of entire functions[J]. Journal of Mathematical Analysis and Application, 2006, 313(1): 24–37 (in Chinese). · Zbl 1087.30023 · doi:10.1016/j.jmaa.2005.05.038 |
| [8] | Zheng Jian-hua. Dynamics of a Meromorphic Function[M]. Beijing: Tsinghua University Press, 2006 (in Chinese). · Zbl 1087.30023 |
| [9] | Polya G. On an integral function of an integral function[J]. Journal of the London Mathematical Society, 1926, 1: 12–15. · JFM 52.0317.06 · doi:10.1112/jlms/s1-1.1.12 |
| [10] | Bergweiler W, Wang Yue-fei. On the dynamics of composite entire functions[J]. Arkiv för Matematik, 1998, 36(1): 31–39. · Zbl 0906.30025 · doi:10.1007/BF02385665 |
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