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Conformal Geometry and Dynamics

ISSN 1088-4173



Potential theory and a characterization of polynomials in complex dynamics

Authors: Yûsuke Okuyama and Małgorzata Stawiska
Journal: Conform. Geom. Dyn. 15 (2011), 152-159
MSC (2010): Primary 37F10; Secondary 31A05
Published electronically: October 4, 2011
MathSciNet review: 2846305
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Abstract: We obtain a characterization of polynomials among rational functions on $\mathbb {P}^1$ from the point of view of complex dynamics and potential theory. This characterization generalizes a theorem of Lopes. Our proof applies both classical and (dynamically) weighted potential theory.

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Additional Information

Yûsuke Okuyama
Affiliation: Division of Mathematics, Graduate School of Science and Technology, Kyoto Institute of Technology, Kyoto 606-8585 Japan

Małgorzata Stawiska
Affiliation: Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Lawrence, Kansas 66045
Address at time of publication: Mathematical Reviews, 416 Fourth St., Ann Arbor, Michigan 48103
ORCID: 0000-0001-5704-7270

Keywords: Balanced measure, harmonic measure, complex dynamics, Lopes’ theorem, Brolin’s theorem, weighted potential theory
Received by editor(s): December 14, 2010
Published electronically: October 4, 2011
Additional Notes: The first author was partially supported by JSPS Grant-in-Aid for Young Scientists (B), 21740096.
The second author thanks the Department of Mathematics of the University of Kansas for supporting her as a Robert D. Adams Visiting Assistant Professor in the years 2008–2011.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.