The g-periodic subvarieties for an automorphism g of positive entropy on a compact Kähler manifold

For a compact Kähler manifold X and a strongly primitive automorphism g of positive entropy, it is shown that X has at most ρ(X) of g-periodic prime divisors. When X is a projective threefold, every prime divisor containing infinitely many g-periodic curves, is shown to be g-periodic (a result in the spirit of the Dynamic Manin–Mumford conjecture as in Zhang (2006) [17]).