Growth rate of ample heights and the dynamical Mordell-Lang type conjecture

Abstract: We provide an explicit formula on the growth rate of ample heights of rational points under iteration of endomorphisms on smooth projective varieties over number fields. As an application, we give a positive answer to a problem of Dynamical Mordell-Lang type for pairs of \'etale endomorphisms, which is a variant of the original one stated by Bell, Ghioca, and Tucker in their monograph.