Dynamics on Bungee set, Escaping set and Filled Julia set of Composite Transcendental Entire Functions

TL;DR

This paper explores the dynamics of composite transcendental entire functions, focusing on Bungee, Escaping, and Filled Julia sets, revealing conditions for their equality and relations among these sets.

Contribution

It introduces new classes of permutable entire functions with equal Bungee sets and establishes relations between the sets of composite and individual functions.

Findings

Bungee sets of certain permutable functions are equal.

Escaping set of composite equals union of individual escaping sets.

Relations between Bungee, Escaping, and Filled Julia sets are established.

Abstract

In this paper, we have investigated the Bungee set of composition of two transcendental entire functions. We have provided a class of permutable entire functions for which their Bungee sets are equal. Moreover, we have obtained a result on permutable entire functions for which the escaping set of the composite entire function equals the union of the escaping sets of the two functions. In addition, we establish important relations between the Bungee set, Escaping set and Filled Julia set of composite entire functions with that of its individual functions.