Brolin's theorem for curves in two complex dimensions

Charles Favre[1]; Mattias Jonsson[2]

  • [1] Université Paris VII, UFR de Mathématiques, Équipe Géométrie et Dynamique, 75251 Paris Cedex 05 (France)
  • [2] University of Michigan, Department of Mathematics, Ann Arbor MI 48109-1109 (USA)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 5, page 1461-1501
  • ISSN: 0373-0956

Abstract

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Given a holomorphic mapping f : ℙ 2 → ℙ 2 of degree d ≥ 2 we give sufficient conditions on a positive closed (1,1) current of S of unit mass under which d - n f n * S converges to the Green current as n → ∞ . We also conjecture necessary condition for the same convergence.

How to cite

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Favre, Charles, and Jonsson, Mattias. "Brolin's theorem for curves in two complex dimensions." Annales de l’institut Fourier 53.5 (2003): 1461-1501. <http://eudml.org/doc/116078>.

@article{Favre2003,
abstract = {Given a holomorphic mapping $f:\{\mathbb \{P\}\}^2\rightarrow \{\mathbb \{P\}\}^2$ of degree $d\ge 2$ we give sufficient conditions on a positive closed (1,1) current of $S$ of unit mass under which $d^\{-n\}f^\{n*\}S$ converges to the Green current as $n\rightarrow \infty $. We also conjecture necessary condition for the same convergence.},
affiliation = {Université Paris VII, UFR de Mathématiques, Équipe Géométrie et Dynamique, 75251 Paris Cedex 05 (France); University of Michigan, Department of Mathematics, Ann Arbor MI 48109-1109 (USA)},
author = {Favre, Charles, Jonsson, Mattias},
journal = {Annales de l’institut Fourier},
keywords = {holomorphic dynamics; currents; Lelong numbers; equidistribution; Kilseman numbers; volume estimates; asymptotic multiplicities; Kiselman numbers},
language = {eng},
number = {5},
pages = {1461-1501},
publisher = {Association des Annales de l'Institut Fourier},
title = {Brolin's theorem for curves in two complex dimensions},
url = {http://eudml.org/doc/116078},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Favre, Charles
AU - Jonsson, Mattias
TI - Brolin's theorem for curves in two complex dimensions
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 5
SP - 1461
EP - 1501
AB - Given a holomorphic mapping $f:{\mathbb {P}}^2\rightarrow {\mathbb {P}}^2$ of degree $d\ge 2$ we give sufficient conditions on a positive closed (1,1) current of $S$ of unit mass under which $d^{-n}f^{n*}S$ converges to the Green current as $n\rightarrow \infty $. We also conjecture necessary condition for the same convergence.
LA - eng
KW - holomorphic dynamics; currents; Lelong numbers; equidistribution; Kilseman numbers; volume estimates; asymptotic multiplicities; Kiselman numbers
UR - http://eudml.org/doc/116078
ER -

References

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