Leírás
The main aim of the Thesis is to demonstrate the diverse applicability
of fractals in different areas of mathematics. Namely,
- widen the class of planar self-affine carpets for which we can
calculate the different dimensions especially in the presence of
overlapping cylinders,
- perform multifractal analysis for the pointwise Hölder exponent of a
family of continuous parameterized fractal curves in \R^d including
deRham's curve,
- show how hierarchical structure can be used to determine the
asymptotic growth of the distance between two vertices and the
diameter of a random graph model, which can be derived from the
Apollonian circle packing problem.
I will present the results in an informal way, illustrated with plenty
of examples, and some hints about the heuristics of the proofs.
Thesis advisor: Károly Simon