Wandering Fatou Components and Algebraic Julia Sets

Details Wandering Fatou Components and Algebraic Julia Sets Wandering Fatou Components and Algebraic Julia Sets

2009-09-24

arxiv.org/abs/0909.4528v2

Mathematics

Dynamical Systems

40 pages, 1 figure, results stated in a slightly more general context

Scientific paper

We study the dynamics of polynomials with coefficients in a non-Archimedean field $K,$ where $K$ is a field containing a dense subset of algebraic elements over a discrete valued field $k.$ We prove that every wandering Fatou component is contained in the basin of a periodic orbit. We obtain a complete description of the new Julia set points that appear when passing from $K$ to the Berkovich line over $K$. We give a dynamical characterization of polynomials having algebraic Julia sets. More precisely, we establish that a polynomial with algebraic coefficients has algebraic Julia set if every critical element is nonrecurrent.

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