Manfred Denker
Institut für Mathematische Stochastik
Georg-August-Universität
Göttingen
Fractal Sets and Boundary Theory
Abstract
We discuss how the concept of a boundary can be used to describe
fractal sets. This is done by two examples: 1. Polynomial endomorphisms
of C2 and their
Julia sets 2. Selfsimilar fractals, in particular the Sierpinski
gasket. The boundaries used are Shilov-, Martin-, Furstenberg-
and Poisson-boundaries. We will show some pictures of the fractal sets
arising in 1. which show many features which still are not quite well
understood.
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