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We prove that every Salem number can be realized as the first dynamicaldegree of an automorphism of a complex simple abelian variety. Also by usingthe similar technique, we prove that the set of first dynamical degrees ofautomorphisms of complex simple abelian varieties except 1 has the minimumvalue 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 areinspired by the work of Nguyen-Bac Dang and Thorsten Herrig.

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