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Let K be a non-archimedean field, and let f in K(z) be a polynomial or rational function of degree at least 2. We present a necessary and sufficient condition, involving only the fixed points of f and their preimages, that determines whether or not the dynamical system f on P^1 has potentially good reduction.
Let K be a non-archimedean field, and let f in K(z) be a rational function of degree d>1. If f has potentially good reduction, we give an upper bound, depending only on d, for the minimal degree of an extension L/K such that f is conjugate over L to
Let $f_1,...,f_gin {mathbb C}(z)$ be rational functions, let $Phi=(f_1,...,f_g)$ denote their coordinatewise action on $({mathbb P}^1)^g$, let $Vsubset ({mathbb P}^1)^g$ be a proper subvariety, and let $P=(x_1,...,x_g)in ({mathbb P}^1)^g({mathbb C})$
We present a p-adic and non-archimdean version of the Five Islands Theorem for meromorphic functions from Ahlfors theory of covering surfaces. In the non-archimedean setting, the theorem requires only four islands, with explicit constants. We present
We formulate a general question regarding the size of the iterated Galois groups associated to an algebraic dynamical system and then we discuss some special cases of our question.
Let $K$ be a number field, let $S$ be a finite set of places of $K$, and let $R_S$ be the ring of $S$-integers of $K$. A $K$-morphism $f:mathbb{P}^1_Ktomathbb{P}^1_K$ has simple good reduction outside $S$ if it extends to an $R_S$-morphism $mathbb{P}