Measures of maximal entropy for meromorphic maps on compact Kähler manifolds

Let $f$ be a dominant meromorphic self-map of a compact Kähler manifold. Assume that $f$ has a strictly dominant intermediate dynamical degree $\lambda$ and that the number of isolated $n$-periodic points, counted with multiplicity, is at most ${\lambda }^n+o({\lambda }^n)$. Then $f$ admits at most one adapted invariant probability measure of entropy $\log \lambda$. If such a measure exists, its natural extension is Bernoulli, and the isolated periodic points equidistribute towards it when counted with or without multiplicity. We apply this criterion to several classes of maps in complex dynamics, resolving longstanding open problems.