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%0 Thesis
%A Jung, Wolf
%T Homeomorphisms on edges of the Mandelbrot set
%C Aachen
%I Publikationsserver der RWTH Aachen University
%M RWTH-CONV-119062
%P 172 S. : Ill., graph. Darst.
%D 2002
%Z Aachen, Techn. Hochsch., Diss., 2002
%X Consider the iteration of complex quadratic polynomials. They form a one-parameter family, and the Mandelbrot set is defined as a subset of the parameter plane: it contains those parameters, such that the Julia set of the corresponding polynomial is connected. Homeomorphisms of subsets of the Mandelbrot set are constructed by quasi-conformal surgery in the dynamic plane. These homeomorphisms have the new property that they are mapping some set onto itself in a non-trivial way, resulting in a countable family of pairwise homeomorphic fundamental domains. Edges and frames are families of subsets, which are constructed combinatorially, and which are pairwise homeomorphic. Moreover, homeomorphisms at Misiurewicz points are constructed, which provide repelling dynamics in the parameter plane. This property is compared to the known asymptotic self-similarity.
%F PUB:(DE-HGF)11
%9 Dissertation / PhD Thesis
%U https://publications.rwth-aachen.de/record/56990