Periodic points and normal families
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- by Detlef Bargmann and Walter Bergweiler PDF
- Proc. Amer. Math. Soc. 129 (2001), 2881-2888 Request permission
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.References
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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
- MR Author ID: 35350
- Email: bergweiler@math.uni-kiel.de
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2881-2888
- MSC (2000): Primary 30D05, 30D45, 37F10
- DOI: https://doi.org/10.1090/S0002-9939-01-05864-6
- MathSciNet review: 1840089