Meromorphic functions with linearly distributed values and Julia sets of rational functions
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- by Walter Bergweiler and Alexandre Eremenko PDF
- Proc. Amer. Math. Soc. 137 (2009), 2329-2333 Request permission
Abstract:
If the preimage of a four-point set under a meromorphic function belongs to the real line, then the image of the real line is contained in a circle in the Riemann sphere. We include an application of this result to holomorphic dynamics: if the Julia set of a rational function is contained in a smooth curve, then it is contained in a circle.References
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Additional Information
- Walter Bergweiler
- Affiliation: Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, D–24098 Kiel, Germany
- MR Author ID: 35350
- Email: bergweiler@math.uni-kiel.de
- Alexandre Eremenko
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 63860
- Email: eremenko@math.purdue.edu
- Received by editor(s): September 2, 2008
- Published electronically: December 22, 2008
- Additional Notes: The first author was supported by the G.I.F., the German-Israeli Foundation for Scientific Research and Development, Grant G-809-234.6/2003; the EU Research Training Network CODY; and the ESF Research Networking Programme HCAA
The second author was supported by NSF grant DMS-0555279 - Communicated by: Mario Bonk
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2329-2333
- MSC (2000): Primary 30D35
- DOI: https://doi.org/10.1090/S0002-9939-08-09788-8
- MathSciNet review: 2495266