On a characterization of polynomials among rational functions in non-archimedean dynamics

Abstract

We study a question on characterizing polynomials among rational functions of degree $>1$ on the projective line over an algebraically closed field that is complete with respect to a non-trivial and non-archimedean absolute value, from the viewpoint of dynamics and potential theory on the Berkovich projective line.

20 pages. (v2) The title is slightly modified because of the focus on the non-archimedean dynamics. Lemma 3.5 in v1 appears now as Lemma 4.2 in this version

References in corpus (2)

• Quantitative approximations of the Lyapunov exponent of a rational function over valued fields
• Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics