Fatou Set, Julia Set and Escaping Set in Holomorphic Subsemigroup Dynamics

2018/07/12 by Bishnu Hari Subedi, Ajaya Kumar Singh, Subedi, Bishnu Hari +1 · 1 citation
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #semigroups and automata theory #Cellular Automata and Applications

paper · pdf · doi:10.48550/arxiv.1807.04499

Abstract

We investigate to what extent Fatou set, Julia set and escaping set of transcendental semigroup is respectively equal to the Fatou set, Julia set and escaping set of its subsemigroup. We define partial fundamental set and fundamental set of transcendental semigroup and on the basis of this set, we prove that Fatou set and escaping set of transcendental semigroup S are non-empty.

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

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