Brolin's theorem for curves in two complex dimensions
Annales de l'Institut Fourier, Volume 53 (2003) no. 5, p. 1461-1501

Given a holomorphic mapping f: 2 2 of degree d2 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: 2 2 de degré d2 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 : https://doi.org/10.5802/aif.1985
Classification:  37F10,  32U25
Keywords: holomorphic dynamics, currents, Lelong numbers, equidistribution, Kilseman numbers, volume estimates, asymptotic multiplicities
@article{AIF_2003__53_5_1461_0,
     author = {Favre, Charles and Jonsson, Mattias},
     title = {Brolin's theorem for curves in two complex dimensions},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {5},
     year = {2003},
     pages = {1461-1501},
     doi = {10.5802/aif.1985},
     zbl = {02014683},
     mrnumber = {2032940},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2003__53_5_1461_0}
}
Favre, Charles; Jonsson, Mattias. Brolin's theorem for curves in two complex dimensions. Annales de l'Institut Fourier, Volume 53 (2003) no. 5, pp. 1461-1501. doi : 10.5802/aif.1985. http://www.numdam.org/item/AIF_2003__53_5_1461_0/

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