Escaping set and Julia set of transcendental semigroups
Dinesh Kumar, Sanjay Kumar, Kin Keung Poon
TL;DR
This paper explores the dynamics of transcendental entire function semigroups, focusing on their escaping and Julia sets, and introduces conditions for invariance, hyperbolicity, and the absence of wandering domains.
Contribution
It provides new criteria for invariance of sets, analyzes limit functions and postsingular sets, and characterizes hyperbolic and postsingularly bounded semigroups.
Findings
Conditions for complete invariance of escaping and Julia sets
Criteria for non-existence of wandering domains
Characterization of hyperbolic and postsingularly bounded semigroups
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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Taxonomy
TopicsMathematical Dynamics and Fractals · Meromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems