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

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

2004-09-16

arxiv.org/abs/math/0409272v2

Mathematics

Dynamical Systems

32 pages, to appear in Ann. Inst. Fourier

Scientific paper

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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