Potential theory and a characterization of polynomials in complex dynamics

Okuyama, Yûsuke; Stawiska, Małgorzata

doi:10.1090/S1088-4173-2011-00230-X

Potential theory and a characterization of polynomials in complex dynamics
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by Yûsuke Okuyama and Małgorzata Stawiska

Conform. Geom. Dyn. 15 (2011), 152-159

DOI: https://doi.org/10.1090/S1088-4173-2011-00230-X

Published electronically: October 4, 2011

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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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