DUMITRU, Dan, SOME ESTIMATIONS OF THE MANDELBROT SET

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Quasiregular Mappings of Polynomial Type in R

Complex dynamics deals with the iteration of holomorphic functions. As is well known, the first functions to be studied which gave non-trivial dynamics were quadratic polynomials, which produced beautiful computer generated pictures of Julia sets and the Mandelbrot set. In the same spirit, this article aims to study the dynamics of the simplest non-trivial quasiregular mappings. These are mappi...

Quasi-Mandelbrot sets for perturbed complex analytic maps: visual patterns

We consider perturbations of the complex quadratic map $ z \to z^2 +c$ and corresponding changes in their quasi-Mandelbrot sets. Depending on particular perturbation, visual forms of quasi-Mandelbrot set changes either sharply (when the perturbation reaches some critical value) or continuously. In the latter case we have a smooth transition from the classical form of the set to some forms, cons...

Fractal Models of Foam Coverage for Ocean Microwave Remote Sensing

Introduction. Methods of fractal geometry are widely used in geophysics and remote sensing for analyses of natural objects and dynamical systems beginning from the fundamental works of Mandelbrot [1]. In particular, in the mid 1990s, a number of authors [2, 3, 4, 5] established an idea that wave breaking and foam/whitecap fields observed in stormy oceans have a universal (multi)fractal characte...

Internal Addresses of the Mandelbrot Set and Galois Groups of Polynomials

We describe an interesting interplay between symbolic dynamics, the structure of the Mandelbrot set, permutations of periodic points achieved by analytic continuation, and Galois groups of certain polynomials. In the early 1990’s, Devaney asked the question: how can you tell where in the Mandelbrot set a given external ray lands, without having Adrien Douady at your side? We provide an answer t...