Wandering Fatou Components and Algebraic Julia Sets

Eugenio Trucco

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arXiv · 0909.4528

Wandering Fatou Components and Algebraic Julia Sets

Eugenio Trucco

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Abstract

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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BibTeX RIS

Eugenio Trucco. 2010-05-13. Wandering Fatou Components and Algebraic Julia Sets. https://arxiv.org/abs/0909.4528

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