On perturbations of the Mandelbrot map

Abstract

In this work, we propose new applications of analytic and non-analytic perturbations of the Mandelbrot map as expressed in a two-parameter deformation family of it. The influence of alternative applications of noise for specific choices of a Mandelbrot set is also provided. Hence, we are in a position of examining the stability of this set under stochastic perturbations. (C) 2000 Elsevier Science Ltd. All rights reserved.