Dynamical degrees of automorphisms of complex simple abelian varieties and Salem numbers

We prove that every Salem number can be realized as the first dynamical degree of an automorphism of a complex simple abelian variety. Also by using the similar technique, we prove that the set of first dynamical degrees of automorphisms of complex simple abelian varieties except 1 has the minimum value when fixing the dimension of complex simple abelian varieties. Moreover, we prove that there is an automorphism of a complex simple abelian variety, whose first dynamical degree is as close as possible to 1. These results are inspired by the work of Nguyen-Bac Dang and Thorsten Herrig. • All Salem numbers can be realized as the first dynamical degrees of an automorphism of a complex simple abelian variety. • The set of the first dynamical degrees, which are larger than 1, of automorphisms of complex simple abelian varieties has the minimum value.