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Non-Real Periodic Points of Entire Functions

Published online by Cambridge University Press:  20 November 2018

Walter Bergweiler
Walter Bergweiler*
Affiliation:
Fachbereich Mathematik, Sekr. MA 8-2, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany
*
*Present address: Mathematisches Seminar Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany, email: [email protected]
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Abstract

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It is shown that if f is an entire transcendental function, l a straight line in the complex plane, and n ≥ 2, then f has infinitely many repelling periodic points of period n that do not lie on l.

Keywords

30D0558F23
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 3 , 01 September 1997 , pp. 271 - 275
Copyright
Copyright © Canadian Mathematical Society 1997

Footnotes

Supported by a Heisenberg Fellowship of the Deutsche Forschungsgemeinschaft.

References

1. Baker, I. N., The distribution of fixpoints of entire functions, Proc. London Math. Soc. (3) 16 (1966), 493–506.Google Scholar
2. Bergweiler, W., Periodic points of entire functions: proof of a conjecture of Baker, Complex Variables Theory Appl. 17 (1991), 57–72.Google Scholar
3. Bergweiler, W., Clunie, J., and Langley, J., Proof of a conjecture of Baker concerning the distribution of fixpoints, Bull. London Math. Soc. 27 (1995), 148–154.Google Scholar
4. Hayman, W. K., Meromorphic Functions, The Clarendon Press, Oxford, 1964.Google Scholar
5. Hayman, W. K., Research Problems in Function Theory, The Athlone Press, London, 1967.Google Scholar
6. Nevanlinna, R., Eindeutige analytische Funktionen, Springer, Berlin, Göttingen, Heidelberg 1953.Google Scholar