*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.