On perturbations of the Mandelbrot map
type: Item
instance of: scholarly article
title: On perturbations of the Mandelbrot map
zbMATH Open document ID: 0962.37022
DOI: 10.1016/S0960-0779(99)00017-X
author: Ioannis Andreadis
author: T. E. Karakasidis
author: John Argyris
published in: Chaos, Solitons and Fractals
publication date: 2000-08-09T00:00:00Z
review text: The authors consider the Mandelbrot map, that is \[ x_{n+1}= x_n^2- y_n^2+ c_1, \qquad y_{n+1}= 2x_n y_n+ c_2, \tag{1} \] where \(c_1,c_2\in \mathbb{R}\). They investigate analytic and nonanalytic perturbations of the Mandelbrot set defined by (1). Moreover they study also the influence of noise on the Mandelbrot set. Their numerical analysis supports the stability of the initial Mandelbrot set under noisy perturbations having a small strength. As the strength of the noise increases, the structure of the Mandelbrot set decays and loses its symmetry.
Mathematics Subject Classification ID: 37F45
Mathematics Subject Classification ID: 37H99
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 1486526
zbMATH Keywords: Mandelbrot map
zbMATH Keywords: symmetry
zbMATH Keywords: perturbation
zbMATH Keywords: noise
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Smooth Decomposition of Generalized Fatou Set Explains Smooth Structure in Generalized Mandelbrot Set
cites work: The influence of noise on the correlation dimension of chaotic attractors
cites work: Q4299632
cites work: Q3736578
cites work: Q4299689
cites work: Q3935355
full work available at URL: s0960-0779(99)00017-x
OpenAlex ID: W2051446272
description: scientific article; zbMATH DE number 1486526