Densities of currents and complex dynamics

2019/02/02 by Duc‐Viet Vu, Vu, Duc-Viet
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1902.00666

openalex publication_date 2019/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Dynamique des automorphismes des surfaces K3
• Super-potentials for currents on compact Kaehler manifolds and dynamics of automorphisms
• Super-potentials, densities of currents and number of periodic points\n for holomorphic maps

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