Dimension and measures on sub-self-affine sets
Dynamical Systems
2017-01-31 v1
Abstract
We show that in a typical sub-self-affine set, the Hausdorff and the Minkowski dimensions coincide and equal the zero of an appropriate topological pressure. This gives a partial positive answer to the question of Falconer. We also study the properties of the topological pressure and the existence and the uniqueness of natural measures supported on a sub-self-affine set.
Cite
@article{arxiv.1701.08611,
title = {Dimension and measures on sub-self-affine sets},
author = {Antti Käenmäki and Markku Vilppolainen},
journal= {arXiv preprint arXiv:1701.08611},
year = {2017}
}