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arXiv · 0706.2169

Nonarchimedean Green functions and dynamics on projective space

Shu Kawaguchi·Joseph H. Silverman
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Abstract

Let F: P^N_K --> P^N_K be a morphism of degree d > 1 defined over a field K that is algebraically closed and complete with respect to a nonarchimedean absolute value. We prove that a modified Green function G_F associated to F is Holder continuous on P^N(K) and that the Fatou set F is equal to the set of points at which G_F is locally constant. Further, G_F vanishes precisely on the set of points P such that F has good reduction at every point in the forward orbit of P. We also prove that the iterates of F are locally uniformly Lipschitz on the Fatou set of F.

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Shu Kawaguchi, Joseph H. Silverman. 2007-07-08. Nonarchimedean Green functions and dynamics on projective space. https://arxiv.org/abs/0706.2169

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