Height growth of rational self-maps

Let $K$ be a number field or a function field of a curve. Let $f$ be a dominant rational self-map of a normal projective variety $X$ of dimension $d$ over $K$, and let $h_H\geq1$ be an ample Weil height. Let $λ_1(f)$ denote the first dynamical degree of $f$. We show that there is a constant $C_{f,h_