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Tien-Cuong Dinh; Nessim Sibony
Geometry of currents, intersection theory and dynamics of horizontal-like maps
(Géométrie des courants, théorie d’intersection et dynamique des applications d’allure horizontale)
Annales de l'institut Fourier, 56 no. 2 (2006), p. 423-457, doi: 10.5802/aif.2188
Article PDF | Reviews MR 2226022 | Zbl 1089.37036
Class. Math.: 37F, 32H50, 32U40
Keywords: Structural discs of currents, Green current, equilibrium measure, mixing, entropy.

Résumé - 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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