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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Periodic points and normal families


Authors: Detlef Bargmann and Walter Bergweiler
Journal: Proc. Amer. Math. Soc. 129 (2001), 2881-2888
MSC (2000): Primary 30D05, 30D45, 37F10
Published electronically: February 9, 2001
MathSciNet review: 1840089
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Abstract:

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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Additional Information

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

Walter Bergweiler
Affiliation: Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, D–24098 Kiel, Germany
Email: bergweiler@math.uni-kiel.de

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05864-6
PII: S 0002-9939(01)05864-6
Received by editor(s): September 13, 1999
Received by editor(s) in revised form: January 31, 2000
Published electronically: February 9, 2001
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2001 American Mathematical Society