Overlapping self-affine sets of Kakeya type

Details Overlapping self-affine sets of Kakeya type Overlapping self-affine sets of Kakeya type

2007-10-02

arxiv.org/abs/0710.0442v1

Mathematics

Classical Analysis and ODEs

27 pages, 1 figure. Submitted October 2007

Scientific paper

We compute the Minkowski dimension for a family of self-affine sets on the
plane. Our result holds for every (rather than generic) set in the class.
Moreover, we exhibit explicit open subsets of this class where we allow
overlapping, and do not impose any conditions on the norms of the linear maps.
The family under consideration was inspired by the theory of Kakeya sets.

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