English

Overlapping self-affine sets of Kakeya type

Classical Analysis and ODEs 2017-02-03 v1 Dynamical Systems

Abstract

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.

Keywords

Cite

@article{arxiv.0710.0442,
  title  = {Overlapping self-affine sets of Kakeya type},
  author = {Antti Kaenmaki and Pablo Shmerkin},
  journal= {arXiv preprint arXiv:0710.0442},
  year   = {2017}
}

Comments

27 pages, 1 figure. Submitted October 2007

R2 v1 2026-06-21T09:25:03.289Z