Dimension and measures on sub-self-affine sets
arXiv:1701.08611 · doi:10.1007/s00605-009-0144-9
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.