Homeomorphisms on edges of the Mandelbrot set

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.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2002

Author dc:creator

• Jung, Wolf

Contributors dc:contributor

• Enß, Volker

• info:eu-repo/classification/ddc/510
• Mathematik
• Quasikonforme Chirurgie
• Mandelbrotmenge
• Isomorphie
• Mandelbrot-Menge
• Selbstähnlichkeit

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-119062%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:56990