P-adic uniformalization in algebraic dynamics

Abstract
Let $f: X\to X$ be an endomorphism of a quasiprojective variety and $x$ a point of $X$. As shown by Bell, Ghioca and Tucker, under certain conditions the orbit of $x$ admits a "p-adic uniformization" for a suitable $p$, that is to say, there exists a $p$-adic analytic map from $\mathbb Z_p$ to $X$ such that its value at a positive integer $n$ is $f^n(x)$. We shall survey a few applications of this observation to various questions of algebraic dynamics.