Densities of currents and complex dynamics

Abstract

We extend the Dinh-Sibony notion of densities of currents to the setting where the ambient manifold is not necessarily Kähler and study the intersection of analytic sets from the point of view of densities of currents. As an application, we introduce the notion of exotic periodic points of a meromorphic self-map. We then establish the expected asymptotic for the sum of the number of isolated periodic points and the number of exotic periodic points for holomorphic self-maps with a simple action on the cohomology groups on a compact Kähler manifold. We also show that the algebraic entropy of meromorphic self-maps of compact complex surfaces is a finite bi-meromorphic invariant.

32 pages. We introduce the notion of exotic periodic points of meromorphic self-maps and prove an asymptotic result for the number of periodic points

References in corpus (4)

• Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy
• Super-potentials for currents on compact Kaehler manifolds and dynamics of automorphisms
• Growth of the number of periodic points for meromorphic maps
• Super-potentials, densities of currents and number of periodic points for holomorphic maps