Soit un endomorphisme holomorphe de . Je présenterai une construction géométrique, due à Briend et Duval, d’une mesure de probabilité ayant les propriétés suivantes : reflète la distribution des préimages des points en dehors d’un ensemble exceptionnel algébrique, les points périodiques répulsifs de s’équidistribuent par rapport à et est l’unique mesure d’entropie maximale de .
Let be a holomorphic endomorphism of . I will present a geometric construction, due to Briend and Duval, of a probability measure having the following properties: reflects the distribution of preimages of points outside an algebraic exceptional set, repelling periodic points of equidistribute with respect to and is the unique measure of maximal entropy of .
Mots clés : dynamique holomorphe, mesure d'équilibre, ensemble exceptionnel, entropie
@incollection{SB_2004-2005__47__33_0, author = {Buff, Xavier}, title = {La mesure d'\'equilibre d'un endomorphisme de <span class="mathjax-formula">$\mathbb {P}^k(\mathbb {C})$</span>}, booktitle = {S\'eminaire Bourbaki : volume 2004/2005, expos\'es 938-951}, author = {Collectif}, series = {Ast\'erisque}, note = {talk:939}, pages = {33--69}, publisher = {Soci\'et\'e math\'ematique de France}, number = {307}, year = {2006}, zbl = {1138.32009}, language = {fr}, url = {archive.numdam.org/item/SB_2004-2005__47__33_0/} }
Buff, Xavier. La mesure d’équilibre d’un endomorphisme de $\mathbb {P}^k(\mathbb {C})$, dans Séminaire Bourbaki : volume 2004/2005, exposés 938-951, Astérisque, no. 307 (2006), Exposé no. 939, pp. 33-69. http://archive.numdam.org/item/SB_2004-2005__47__33_0/
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