ABSTRACT
Given a holomorphic endomorphism f : S → S on a Riemann surface S, we consider the dynamical system generated by the iterates of f , denoted fn = f ◦ n. . . ◦ f . There is a dynamically natural partition of the phase space S into the Fatou set F(f), restricted to which the iterates of f form a normal family, and the Julia set J (f) = S−F(f), which is the complement of the Fatou set.
