On iteration of algebraic points under a rational self-map

Let $X$ be an algebraic variety and $f\colon X\to X$ a rational self-map, both defined over a number field $K$. One would like to compare the iterated orbits of “sufficiently general” algebraic points of $X$ with those of sufficiently general complex points. In particular, as the first step in this direction, I shall prove that as soon as $f$ is of infinite order, most of algebraic points on $X$ are non-preperiodic.