Ergodic Theory and Dynamical Systems

Research Article

Entropy properties of rational endomorphisms of the Riemann sphere

M. Ju. Ljubicha1

a1 Department of Mathematics, Kharkov State University, Kharkov, USSR

Abstract

In this paper the existence of a unique measure of maximal entropy for rational endomorphisms of the Riemann sphere is established. The equidistribution of pre-images and periodic points with respect to this measure is proved.

(Received November 10 1981)