Given a holomorphic mapping of degree we give sufficient conditions on a positive closed (1,1) current of of unit mass under which converges to the Green current as . We also conjecture necessary condition for the same convergence.
Pour toute application de degré nous donnons des conditions suffisantes sur un courant positif fermé de bidegré , pour que la suite converge vers le courant de Green lorsque . Nous conjecturons aussi des conditions nécessaires pour ce problème de convergence.
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}, pages = {1461--1501}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {5}, year = {2003}, doi = {10.5802/aif.1985}, mrnumber = {2032940}, zbl = {02014683}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1985/} }
TY - JOUR TI - Brolin's theorem for curves in two complex dimensions JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 1461 EP - 1501 VL - 53 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1985/ UR - https://www.ams.org/mathscinet-getitem?mr=2032940 UR - https://zbmath.org/?q=an%3A02014683 UR - https://doi.org/10.5802/aif.1985 DO - 10.5802/aif.1985 LA - en ID - AIF_2003__53_5_1461_0 ER -
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. https://aif.centre-mersenne.org/articles/10.5802/aif.1985/
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