no. 5
Brolin's theorem for curves in two complex dimensions
[Théorème de Brolin pour les courbes en dimension deux]
Favre, Charles1 ; Jonsson, Mattias2
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, Tome 53 (2003) no. 5, pp. 1461-1501.

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.

Pour toute application f:ℙ 2 →ℙ 2 de degré d≥2 nous donnons des conditions suffisantes sur un courant positif fermé S de bidegré (1,1), pour que la suite d -n f n* S converge vers le courant de Green lorsque n→∞. Nous conjecturons aussi des conditions nécessaires pour ce problème de convergence.

DOI : 10.5802/aif.1985
Classification : 37F10, 32U25
Keywords: holomorphic dynamics, currents, Lelong numbers, equidistribution, Kilseman numbers, volume estimates, asymptotic multiplicities
Mots-clés : dynamique holomorphe, courants, nombre de Lelong, équidistribution, nombre de Kiselman, estimations de volume, multiplicités asymptotiques

Favre, Charles 1 ; Jonsson, Mattias 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) 
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Favre, Charles; Jonsson, Mattias. Brolin's theorem for curves in two complex dimensions. Annales de l'Institut Fourier, Tome 53 (2003) no. 5, pp. 1461-1501. doi : 10.5802/aif.1985. https://aif.centre-mersenne.org/articles/10.5802/aif.1985/

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