## Two characterizations of equilibrium measure of an endomorphism of $$P^k(\mathbb{C})$$. (Deux caractérisations de la mesure d’équilibre d’un endomorphisme de $$P^k(\mathbb{C})$$.)(French. English summary)Zbl 1010.37004

Summary: Let $$\mu$$ be the equilibrium measure of an endomorphism of $$P^k(\mathbb{C})$$. We show that it is its unique measure of maximal entropy. We build $$\mu$$ directly as the distribution of preimages of any point outside an algebraic exceptional set.

### MSC:

 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets

### Keywords:

maximal entropy; distribution of preimages
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