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ISSN 1088-6850(e) ISSN 0002-9947(p)

Weakly repelling fixpoints and the connectivity of wandering domains

Author(s): Walter Bergweiler; Norbert Terglane
Journal: Trans. Amer. Math. Soc. 348 (1996), 1-12.
MSC (1991): Primary 30D05, 58F23
MathSciNet review: 1327252
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Abstract: It is proved that if a transcendental meromorphic function $f$ has a multiply-connected wandering domain, then $f$ has a fixpoint $z_0$ such that $|f'(z_0)|>1$ or $f'(z_0)=1$ . Entire functions with a multiply-connected wandering domain have infinitely many such fixpoints. These results are used to show that solutions of certain differential equations do not have wandering domains at all.

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