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

Abstract

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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.

How to cite

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Dinh, 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 -

References

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