English

Planar self-affine sets with equal Hausdorff, box and affinity dimensions

Dynamical Systems 2016-08-03 v2

Abstract

Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity dimension. We exhibit some new specific classes of self-affine sets for which these dimensions are equal.

Keywords

Cite

@article{arxiv.1503.01270,
  title  = {Planar self-affine sets with equal Hausdorff, box and affinity dimensions},
  author = {Kenneth Falconer and Tom Kempton},
  journal= {arXiv preprint arXiv:1503.01270},
  year   = {2016}
}

Comments

18 pages, 2 figures

R2 v1 2026-06-22T08:44:03.928Z