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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
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