  We show that any dominant meromorphic self-map f of a compact Kaehler
manifold X is an Artin-Mazur map. More precisely, if P_n(f) is the number of
its isolated periodic points of period n (counted with multiplicity), then
P_n(f) grows at most exponentially fast with respect to n and the exponential
rate is at most equal to the algebraic entropy of f. Further estimates are
given when X is a surface. Among the techniques introduced in this paper, the
h-dimension of the density between two arbitrary positive closed currents on a
compact Kaehler surface is obtained.
