Growth of the number of periodic points for meromorphic maps

Abstract

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.

18 pages

References in corpus (4)

• Questions on self maps of algebraic varieties
• Relative dynamical degrees of correspondences over a field of arbitrary characteristic
• (Relative) dynamical degrees of rational maps over an algebraic closed field
• Equidistribution of saddle periodic points for Henon-type automorphisms of C^k

Cited by in corpus (5)

• Super-potentials, densities of currents and number of periodic points for holomorphic maps
• Complexities of differentiable dynamical systems
• Densities of currents and complex dynamics
• Positive plurisubharmonic currents: Generalized Lelong numbers and Tangent theorems
• Hypergeometric Groups and Dynamics on K3 Surfaces