A Brief Study on Julia Sets in the Dynamics of Entire Transcendental Function Using Mann Iterative Scheme

Abstract

In this research, we look at the Julia set patterns that are linked to the entire transcendental function f(z)=aezn+bz+c, where a,b,c∈C and n≥2, using the Mann iterative scheme, and discuss their dynamical behavior. The sophisticated orbit structure of this function, whose Julia set encompasses the entire complex plane, is described using symbolic dynamics. We also present bifurcation diagrams of Julia sets generated using the proposed iteration and function, which altogether contain four parameters, and discuss the graphical analysis of bifurcation occurring in the family of this function.