La mesure d’équilibre d’un endomorphisme de ${\mathbb{P}}^k\left(ℂ\right)$

Buff, Xavier

Séminaire Bourbaki : volume 2004/2005, exposés 938-951, Astérisque, no. 307 (2006), Exposé no. 939, pp. 33-69.

Soit $f$ un endomorphisme holomorphe de ${\mathbb{P}}^k\left(ℂ\right)$. Je présenterai une construction géométrique, due à Briend et Duval, d’une mesure de probabilité $\mu$ ayant les propriétés suivantes : $\mu$ 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 $\mu$ et $\mu$ est l’unique mesure d’entropie maximale de $f$.

Let $f$ be a holomorphic endomorphism of ${\mathbb{P}}^k\left(ℂ\right)$. I will present a geometric construction, due to Briend and Duval, of a probability measure $\mu$ having the following properties: $\mu$ reflects the distribution of preimages of points outside an algebraic exceptional set, repelling periodic points of $f$ equidistribute with respect to $\mu$ and $\mu$ is the unique measure of maximal entropy of $f$.

Classification : 32H50
Mot clés : dynamique holomorphe, mesure d'équilibre, ensemble exceptionnel, entropie
Keywords: holomorphic dynamics, equilibrium measure, exceptional set, entropy

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