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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Weakly repelling fixpoints and the connectivity of wandering domains


Authors: Walter Bergweiler and Norbert Terglane
Journal: Trans. Amer. Math. Soc. 348 (1996), 1-12
MSC (1991): Primary 30D05, 58F23
DOI: https://doi.org/10.1090/S0002-9947-96-01511-5
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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Additional Information

Walter Bergweiler
Affiliation: Lehrstuhl II für Mathematik, RWTH Aachen, D-52056 Aachen, Germany
Address at time of publication: Fachbereich Mathematik, Sekr. MA 8–2, TU Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany
Email: bergweil@math.tu-berlin.de

Norbert Terglane
Affiliation: Lehrstuhl II für Mathematik, RWTH Aachen, D-52056 Aachen, Germany
Email: terglan@math2.rwth-aachen.de

DOI: https://doi.org/10.1090/S0002-9947-96-01511-5
Received by editor(s): August 17, 1993
Article copyright: © Copyright 1996 American Mathematical Society