For a dominant rational self-map on a smooth projective variety defined over a number field, Shu Kawaguchi and Joseph H. Silverman conjectured that the (first) dynamical degree is equal to the arithmetic degree at an algebraic point whose forward orbit is well-defined and Zariski dense. We give some examples of self-maps on product varieties and rational points on them for which the Kawaguchi-Silverman conjecture holds.
"Dynamical degree and arithmetic degree of endomorphisms on product varieties." Tohoku Math. J. (2) 72 (1) 1 - 13, 2020. https://doi.org/10.2748/tmj/1585101618