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

Briend, Jean-Yves; Duval, Julien

Publ. Math., Inst. Hautes Étud. Sci. 93, 145-159 (2001).

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