Proceedings of the American Mathematical Society

Author(s): Detlef Bargmann; Walter Bergweiler
Journal: Proc. Amer. Math. Soc. 129 (2001), 2881-2888.
MSC (2000): Primary 30D05, 30D45, 37F10
Posted: February 9, 2001
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Let $\mathcal{F}$ be the family of all functions which are holomorphic in some domain and do not have periodic points of some period greater than one there. It is shown that $\mathcal{F}$ is quasinormal, and the sequences in $\mathcal{F}$ which do not have convergent subsequences are characterized. The method also yields a new proof of the result that transcendental entire functions have infinitely many periodic points of all periods greater than one.

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Detlef Bargmann
Affiliation: Mathematisches Seminar, Christian--Albrechts--Universität zu Kiel, Ludewig--Meyn--Str. 4, D--24098 Kiel, Germany
Email: bargmann@math.uni-kiel.de

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