On the Julia sets of a noise-perturbed Mandelbrot map

Abstract

In the present work we present numerical results which support further a 2 " -type bifurcation scenario for the interior of the Fatou sets, as suggested by the smooth decomposition method introduced by Peinke, Parisi, Rohricht and Rossler [Z. Naturforsch. 43A (1987) 14-16] when applied to a Mandelbrot map subject to noise with a small strength. As the strength of the noise increases the smooth decomposition methods reveals now a 2 " -type bifurcation scenario for the external region of the Fatou sets, at least in the limit of our numerical results. (C) 2001 Published by Elsevier Science Ltd.