Potential theory and a characterization of polynomials in complex dynamics

Abstract

We obtain a measure theoretical characterization of polynomials among rational functions on ${\mathbb{P}}^1$, which generalizes a theorem of Lopes. Our proof applies both classical and dynamically weighted potential theory.

Rewritten proof of the main theorem, results unchanged. Added references

Cited by in corpus (3)

• Repelling periodic points and logarithmic equidistribution in non-archimedean dynamics
• Lyapunov exponents in complex dynamics and potential theory
• Fekete sequences in complex dynamics