A Study of Fatou Set, Julia set and Escaping Set in Nearly Abelian Transcendental Semigroup

2018/08/01 by Bishnu Hari Subedi, Ajaya Kumar Singh, Subedi, Bishnu Hari +1
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Polynomial and algebraic computation #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1808.00875

openalex publication_date 2018/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We mainly generalize the notion of abelian transcendental semigroup to nearly abelian transcendental semigroup. We prove that Fatou set, Julia set and escaping set of nearly abelian transcendental semigroup are completely invariant. We investigate no wandering domain theorem in such a transcendental semigroup. We also obtain results on a complete generalization of the classification of periodic Fatou components.

Citations

• Escaping Set of Hyperbolic Semigroup
• Fatou Set, Julia Set and Escaping Set in Holomorphic Subsemigroup Dynamics

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