On perturbations of the Mandelbrot map
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.
scientific article; zbMATH DE number 1486526