Dynamical Properties of Morphisms on Higher Dimensional Projective Space over Local Field北大核心CSCD

Let Cv be an algebraically closed non-archimedean field, complete with respect to a valuation v. Let ϕ : PN → PN be a morphism of degree greater than one defined over Cv, Φ a lift of ϕ. Let GΦ be the Green function of Φ and ρ the chordal metric on PN(Cv). In this paper, we first study the properties of reduction of points in high dimensional projective space and reduction of automorphisms of PN with degree one. With the help of Green function GΦ of Φ, we introduce the arithmetic distance of morphisms and investigate its property. The necessary and sufficient condition which Φ has good reduction is obtained in this paper. We also describe explicitly the Filled Julia set of Φ by its Green function. © 2022 Chinese Academy of Sciences. All rights reserved.