On the Julia set of the perturbed Mandelbrot map

Abstract

In this work, we present numerical results which support the smooth decomposition method of the generalized Julia set by Peintge et al., in the case of other perturbations of the Mandelbrot map studied in our previous work (Argyris J, Andreadis I, Karakasidis T. Chaos, Solitons & Fractals 1999). We also calculate the generalized Julia set of a Mandelbrot map subject to noise. Hence, we are in a position to examining numerically the stability of this set under small noise. (C) 2000 Elsevier Science Ltd. All rights reserved.