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.References
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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
- MR Author ID: 35350
- 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
- Received by editor(s): August 17, 1993
- © Copyright 1996 American Mathematical Society
- 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