Dynamical degree and arithmetic degree of endomorphisms on product varieties

Abstract

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.