Equidistribution towards the Green current for holomorphic maps
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 2, pp. 307-336.

Let f be a non-invertible holomorphic endomorphism of a projective space and f n its iterate of order n. We prove that the pull-back by f n of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to f when n tends to infinity. We also give an analogous result for the pull-back of positive closed (1,1)-currents and a similar result for regular polynomial automorphisms of  k .

Soient f un endomorphisme holomorphe non-inversible d’un espace projectif et f n son itéré d’ordre n. Nous prouvons que l’image réciproque par f n d’une hypersurface générique (au sens de Zariski), proprement normalisée, converge vers le courant de Green associé à f quand n tend vers l’infini. Nous donnons également un résultat analogue pour les images réciproques des (1,1)-courants positifs fermés et un résultat similaire pour les automorphismes polynomiaux réguliers de k .

DOI: 10.24033/asens.2069
Classification: 37F10, 32H50, 32U05
Keywords: Green current, exceptional set, plurisubharmonic function, Lelong number, regular automorphism
Mot clés : courants de Green, ensemble exceptionnel, fonction plurisousharmonique, nombre de Lelong, automorphisme régulier
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     author = {Dinh, Tien-Cuong and Sibony, Nessim},
     title = {Equidistribution towards the {Green} current for holomorphic maps},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {307--336},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 41},
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Dinh, Tien-Cuong; Sibony, Nessim. Equidistribution towards the Green current for holomorphic maps. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 2, pp. 307-336. doi : 10.24033/asens.2069. http://www.numdam.org/articles/10.24033/asens.2069/

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