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An entire function with a Baker domain and sparsely distributed singular values

Published online by Cambridge University Press:  01 July 2008

D. S. FLEISCHMANN
D. S. FLEISCHMANN*
Affiliation:
Department of Mathematics, The Open University, Walton Hall, Milton Keynes MK76AA. e-mail: d.s.fleischmann@open.ac.uk
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Abstract

We present an example of an entire function with a Baker domain such that the complement of the set of singular values of the function contains annuli of arbitrarily large width. This is the first known example of a function with this property.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 227 - 241
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

REFERENCES

[1]Baker, I. N.. The iteration of polynomials and transcendental entire functions. J. Austral. Math. Soc. (Series A) 30 (1981), 483–495.CrossRefGoogle Scholar
[2]Bargmann, D.. Normal families of covering maps. J. Anal. Math. 85 (2001), 291–306.CrossRefGoogle Scholar
[3]Beardon, A. F.. Iteration of Rational Functions (Springer Verlag, 1991).CrossRefGoogle Scholar
[4]Bergweiler, W.. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151–188.CrossRefGoogle Scholar
[5]Evgrafov, M. A.. Analytic Functions (Dover Publications Inc. 1978).Google Scholar
[6]Hayman, W. K. and Kennedy, P. B.. Subharmonic Functions (Academic Press Inc. 1976).Google Scholar
[7]Morosawa, S., Nishimura, Y., Taniguchi, M. and Ueda, T.. Holomorphic dynamics (Cambridge University Press, 2000).Google Scholar
[8]Rippon, P. J. and Stallard, G. M.. Singularities of meromorphic functions with Baker domains. Math. Proc. Camb. Phil. Soc. 141 (2006), 371–382.CrossRefGoogle Scholar