A Comparison of Classical Holomorphic Dynamics and Holomorphic Semigroup Dynamics-II

Bishnu Hari Subedi; Ajaya Singh

doi:10.3126/nmsr.v37i1-2.34098

Bishnu Hari Subedi Central Department of Mathematics, Institute of Science and Technology, Tribhuvan University, Kirtipur, Kathmandu
Ajaya Singh Central Department of Mathematics, Institute of Science and Technology, Tribhuvan University, Kirtipur, Kathmandu

DOI: https://doi.org/10.3126/nmsr.v37i1-2.34098

Keywords: Holomorphic semigroup, transcendental semigroup, Fatou set, Julia set, escaping set, S- completely invariant set

Abstract

In this paper, we prove that the escaping set of a transcendental semi group is S-forward invari-ant. We also prove that if a holomorphic semi group is a belian, then the Fatou, Julia, and escaping sets are S-completely invariant. We also investigate certain cases and conditions that the holomorphic semi group dynamics exhibits the similar dynamical behavior just like a classical holomorphic dynamics. Frequently, we also examine certain amount of connections and contrasts between classical holomorphic dynamics and holomorphic semi group dynamics.

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