Equidistribution of preimages for polarized dynamical systems over nonarchimedean fields

Let $K$ be an algebraically closed complete nonarchimedean field, possibly with trivial absolute value, and let $X$ be an irreducible projective variety over $K$. Suppose $f\colon X\to X$ is a flat polarized dynamical system of degree $d\geq 2$. For a point $x\in X^\an$, let $Y\subseteq X$ be the smallest totally invariant Zariski closed set such that $x\in Y^\an\subseteq X^\an$. Let $Y_0\subseteq Y$ be the unique component with $x\in Y_0^\an$, and let $m\geq 1$ satisfy $f^{-m}(Y_0)=Y_0$. Equidistribution conjecture. The iterated $f^m$-preimages of $x$ equidistribute to the Chambert-Loir measure associated with the dynamical system $f^m\colon Y_0^\an\to Y_0^\an$. The statement seeks a nonarchimedean analogue of complex equidistribution of preimages. Existing results establish related equidistribution theorems for rational maps of the Berkovich projective line and for points of small height, while equidistribution of preimages to the Chambert-Loir measure in this generality is not clear from the cited work.