Zeros of power series and connectedness loci for self-affine sets.
Correlation dimension for self-similar Cantor sets with overlaps
We prove a classification theorem of the “Glimm-Effros” type for Borel order relations: a Borel partial order on the reals either is Borel linearizable or includes a copy of a certain Borel partial order which is not Borel linearizable.
On the topology of sums in powers of an algebraic number
The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition
Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.
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