On Completely Invariant Julia Sets of Trascendental Semigroups

Abstract

In holomorphic semigroup dynamics, Julia set is in general backward invariant and so some fundamental results of classical complex dynamics can not be generalized to semigroup dynamics. In this paper, we define completely invariant Julia set of transcendental semigroup and we see how far the results of classical transcendental dynamics generalized to transcendental semigroup dynamics.