La mesure d’équilibre d’un endomorphisme de k ()
[The equilibrium measure of an endomorphism of k ()]
Séminaire Bourbaki : volume 2004/2005, exposés 938-951, Astérisque, no. 307 (2006), Talk no. 939, pp. 33-69.

Let f be a holomorphic endomorphism of k (). I will present a geometric construction, due to Briend and Duval, of a probability measure μ having the following properties: μ reflects the distribution of preimages of points outside an algebraic exceptional set, repelling periodic points of f equidistribute with respect to μ and μ is the unique measure of maximal entropy of f.

Soit f un endomorphisme holomorphe de k (). Je présenterai une construction géométrique, due à Briend et Duval, d’une mesure de probabilité μ ayant les propriétés suivantes : μ reflète la distribution des préimages des points en dehors d’un ensemble exceptionnel algébrique, les points périodiques répulsifs de f s’équidistribuent par rapport à μ et μ est l’unique mesure d’entropie maximale de f.

Classification: 32H50
Keywords: holomorphic dynamics, equilibrium measure, exceptional set, entropy
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Buff, Xavier. La mesure d’équilibre d’un endomorphisme de $\mathbb {P}^k(\mathbb {C})$, in Séminaire Bourbaki : volume 2004/2005, exposés 938-951, Astérisque, no. 307 (2006), Talk no. 939, pp. 33-69. http://archive.numdam.org/item/SB_2004-2005__47__33_0/

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