Periodic points and normal families

Bargmann, Detlef; Bergweiler, Walter

doi:10.1090/S0002-9939-01-05864-6

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.

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