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

Tien-Cuong Dinh^{[1]}; Nessim Sibony^{[2]}

- [1] Institut de Mathématique de Jussieu Plateau 7D, Analyse Complexe 175 rue du Chevaleret 75013 Paris (France)
- [2] Université Paris-Sud Mathématique - Bâtiment 425 UMR 8628 91405 Orsay (France)

Annales de l’institut Fourier (2006)

- Volume: 56, Issue: 2, page 423-457
- ISSN: 0373-0956

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topDinh, Tien-Cuong, and Sibony, Nessim. "Geometry of currents, intersection theory and dynamics of horizontal-like maps." Annales de l’institut Fourier 56.2 (2006): 423-457. <http://eudml.org/doc/10152>.

@article{Dinh2006,

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.},

affiliation = {Institut de Mathématique de Jussieu Plateau 7D, Analyse Complexe 175 rue du Chevaleret 75013 Paris (France); Université Paris-Sud Mathématique - Bâtiment 425 UMR 8628 91405 Orsay (France)},

author = {Dinh, Tien-Cuong, Sibony, Nessim},

journal = {Annales de l’institut Fourier},

keywords = {Structural discs of currents; Green current; equilibrium measure; mixing; entropy; topological entropy; intersection of currents; Green currents; horizontal-like mappings; extremality properties},

language = {eng},

number = {2},

pages = {423-457},

publisher = {Association des Annales de l’institut Fourier},

title = {Geometry of currents, intersection theory and dynamics of horizontal-like maps},

url = {http://eudml.org/doc/10152},

volume = {56},

year = {2006},

}

TY - JOUR

AU - Dinh, Tien-Cuong

AU - Sibony, Nessim

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

JO - Annales de l’institut Fourier

PY - 2006

PB - Association des Annales de l’institut Fourier

VL - 56

IS - 2

SP - 423

EP - 457

AB - 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.

LA - eng

KW - Structural discs of currents; Green current; equilibrium measure; mixing; entropy; topological entropy; intersection of currents; Green currents; horizontal-like mappings; extremality properties

UR - http://eudml.org/doc/10152

ER -

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