2014•arXiv (Cornell University)Open access

Escaping set and Julia set of transcendental semigroups

Dinesh Kumar, Sanjay Kumar, Kin‐Keung Poon

Abstract

We discuss the dynamics of semigroups of transcendental entire functions using Fatou-Julia theory and provide a condition for the complete invariance of escaping set and Julia set of transcendental semigroups. Results regarding limit functions and postsingular set are also derived. In addition, classes of hyperbolic and postsingularly bounded transcendental semigroups are given. We also provide certain criterion for non existence of wandering domains of transcendental semigroups.

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Key concepts: Transcendental number, Julia set, Mathematics, Special classes of semigroups, Entire function, Bounded function, Set (abstract data type), Transcendental function