The equilibrium measure of an endomorphism of ℙ k ( ℂ )

Xavier Buff

Séminaire Bourbaki (2004-2005)

  • Volume: 47, page 33-70
  • ISSN: 0303-1179

Abstract

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Let f be a holomorphic endomorphism of ℙ k ( ℂ ) . I will present a geometric construction, due to Briend and Duval, of a probability measure μ having the following properties: μ reflects the distribution of preimages of points outside an algebraic exceptional set, repelling periodic points of f equidistribute with respect to μ and μ is the unique measure of maximal entropy of f .

How to cite

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Buff, Xavier. "La mesure d’équilibre d’un endomorphisme de $\mathbb {P}^k(\mathbb {C})$." Séminaire Bourbaki 47 (2004-2005): 33-70. <http://eudml.org/doc/252174>.

@article{Buff2004-2005,
abstract = {Soit $f$ un endomorphisme holomorphe de $\mathbb \{P\}^k(\mathbb \{C\})$. Je présenterai une construction géométrique, due à Briend et Duval, d’une mesure de probabilité $\mu $ ayant les propriétés suivantes : $\mu $ reflète la distribution des préimages des points en dehors d’un ensemble exceptionnel algébrique, les points périodiques répulsifs de $f$ s’équidistribuent par rapport à $\mu $ et $\mu $ est l’unique mesure d’entropie maximale de $f$.},
author = {Buff, Xavier},
journal = {Séminaire Bourbaki},
keywords = {holomorphic dynamics; equilibrium measure; exceptional set; entropy},
language = {fre},
pages = {33-70},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {La mesure d’équilibre d’un endomorphisme de $\mathbb \{P\}^k(\mathbb \{C\})$},
url = {http://eudml.org/doc/252174},
volume = {47},
year = {2004-2005},
}

TY - JOUR
AU - Buff, Xavier
TI - La mesure d’équilibre d’un endomorphisme de $\mathbb {P}^k(\mathbb {C})$
JO - Séminaire Bourbaki
PY - 2004-2005
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 47
SP - 33
EP - 70
AB - Soit $f$ un endomorphisme holomorphe de $\mathbb {P}^k(\mathbb {C})$. Je présenterai une construction géométrique, due à Briend et Duval, d’une mesure de probabilité $\mu $ ayant les propriétés suivantes : $\mu $ reflète la distribution des préimages des points en dehors d’un ensemble exceptionnel algébrique, les points périodiques répulsifs de $f$ s’équidistribuent par rapport à $\mu $ et $\mu $ est l’unique mesure d’entropie maximale de $f$.
LA - fre
KW - holomorphic dynamics; equilibrium measure; exceptional set; entropy
UR - http://eudml.org/doc/252174
ER -

References

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