Normality and repelling periodic points

Chang, Jianming; Zalcman, Lawrence

doi:10.1090/S0002-9947-2011-05280-3

Normality and repelling periodic points
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by Jianming Chang and Lawrence Zalcman

Trans. Amer. Math. Soc. 363 (2011), 5721-5744

DOI: https://doi.org/10.1090/S0002-9947-2011-05280-3

Published electronically: June 17, 2011

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Abstract:

Let $k\geq 3(\geq 2)$ be an integer and $\mathcal {F}$ be a family of functions meromorphic in a domain $D\subset \mathbb {C}$, all of whose poles have multiplicity at least 2 (at least 3). If in $D$ each $f\in \mathcal {F}$ has neither repelling fixed points nor repelling periodic points of period $k$, then $\mathcal {F}$ is a normal family in $D$. Examples are given to show that the conditions on poles are necessary and sharp.

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