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We establish an equidistribution result for the pull-back of a (1,1)-closed positive current in ℂ² by a proper polynomial map of small topological degree. We also study convergence at infinity on good compactifications of ℂ². We make use of a lemma that enables us to control the blow-up of some integrals in the neighborhood of a big logarithmic singularity of a plurisubharmonic function. Finally, we discuss the importance of the properness hypothesis, and we give some results in the case where this hypothesis is omitted.
Frédéric Protin. "Équidistribution vers le courant de Green." Annales Polonici Mathematici 115.3 (2015): 201-218. <http://eudml.org/doc/280152>.
@article{FrédéricProtin2015, author = {Frédéric Protin}, journal = {Annales Polonici Mathematici}, keywords = {complex dynamics; green's current; Lelong number}, language = {fre}, number = {3}, pages = {201-218}, title = {Équidistribution vers le courant de Green}, url = {http://eudml.org/doc/280152}, volume = {115}, year = {2015}, }
TY - JOUR AU - Frédéric Protin TI - Équidistribution vers le courant de Green JO - Annales Polonici Mathematici PY - 2015 VL - 115 IS - 3 SP - 201 EP - 218 LA - fre KW - complex dynamics; green's current; Lelong number UR - http://eudml.org/doc/280152 ER -