Nonarchimedean Green Functions and Dynamics on Projective Space
نویسندگان
چکیده
Abstract. Let φ : PNK → P N K be a morphism of degree d ≥ 2 defined over a field K that is algebraically closed field and complete with respect to a nonarchimedean absolute value. We prove that a modified Green function ĝφ associated to φ is Hölder continuous on P (K) and that the Fatou set F(φ) of φ is equal to the set of points at which ĝΦ is locally constant. Further, ĝφ vanishes precisely on the set of points P such that φ has good reduction at every point in the forward orbit Oφ(P ) of P . We also prove that the iterates of φ are locally uniformly Lipschitz on F(φ).
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