  For any given Salem number, we construct an automorphism on a simple abelian
variety whose first dynamical degree is the square of the Salem number. Our
construction works for both simple abelian varieties with totally indefinite
quaternion multiplication and for simple abelian varieties of the second kind.
We then give a complete classification of the dynamical degree sequences for
abelian varieties of dimension at most four and obtain an ergodic result for
sequences of pullbacks of forms.
