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.
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