Analytical Study of the Julia Set of a Coupled Generalized Logistic Map

Abstract

A coupled system of two generalized logistic maps is studied. In particular influence of the coupling to the behaviour of the Julia set in two dimensional complex space is analyzed. It is proved analytically that the Julia set disappears from the complex plane uniformly as a parameter, which interpolates between chaotic phase and integrable phase, approaches to the critical value as far as the coupling strength satisfies a certain condition.