Weakly repelling fixpoints and the connectivity of wandering domains

Bergweiler, Walter; Terglane, Norbert

doi:10.1090/S0002-9947-96-01511-5

Weakly repelling fixpoints and the connectivity of wandering domains
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by Walter Bergweiler and Norbert Terglane PDF

Trans. Amer. Math. Soc. 348 (1996), 1-12 Request permission

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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