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Some entire functions with multiply-connected wandering domains

Published online by Cambridge University Press:  19 September 2008

I. N. Baker
I. N. Baker
Affiliation:
Department of Mathematics, Imperial College of Science and Technology, University of London, London SW7 2BZ, England
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Abstract

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A component U of the complement of the Julia set of an entire function ƒ is a wandering domain if the sets ƒn(U) are mutually disjoint, where n ∈ℕ and ƒn is the n-th iterate of ƒ. Examples are given of entire ƒ of order , which have multiply-connected wandering domains. An example is given where the connectivity is infinite.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 2 , June 1985, pp. 163 - 169
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Baker, I. N.. The domains of normality of an entire function. Ann. Acad. Sci. Fenn. Ser. AI. Math. 1 (1975), 277–283.Google Scholar
[2]Baker, I. N.. An entire function which has wandering domains. J. Australian Math. Soc. (Ser. A) 22 (1976), 173–176.CrossRefGoogle Scholar
[3]Baker, I. N.. Wandering domains in the iteration of entire functions, (a) Institut Mittag-Leffler Report No. 20, 1983. (b) Proc. London Math. Soc. (3), 49 (1984), 563–576.CrossRefGoogle Scholar
[4]Eremenko, A. E. & Ljubič, M. Yu.. Iterates of entire functions (Russian). Preprint, Physico-Tech. Inst. Low Temperatures, Ukr SSR Academy of Sciences, Kharkov, 1984, No. 6.Google Scholar
[5]Fatou, P.. Sur les équations fonctionelles. Bull. Soc. Math. France, 47 (1919), 161–271; 48 (1920), 33–94 and 208–314.CrossRefGoogle Scholar
[6]Fatou, P.. Sur l'itérations des fonctions transcendantes entiéres. Acta Math. 47 (1926), 337–370.CrossRefGoogle Scholar
[7]Sullivan, D.. Quasiconformal homeomorphisms and dynamics I. Solution of the Fatou-Julia problem on wandering domains. I.H.E.S. preprint M/82/59 November 1982.Google Scholar