%0 Journal Article
%T Wandering Fatou Components and Algebraic Julia Sets
%A Eugenio Trucco
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0909.4528v2