Geometry of currents, intersection theory and dynamics of horizontal-like maps

2004/09/16 by Tien‐Cuong Dinh, Nessim Sibony, Dinh, Tien-Cuong +1
Mathematics · #Advanced Topology and Set Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0409272

openalex publication_date 2004/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a geometry on the cone of positive closed currents of bidegree (p,p) and apply it to define the intersection of such currents. We also construct and study the Green currents and the equilibrium measure for horizontal-like mappings. The Green currents satisfy some extremality properties. The equilibrium measure is invariant, mixing and has maximal entropy. It is equal to the intersection of the Green currents associated to the horizontal-like map and to its inverse.

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