Intersections of certain deleted digits sets
Metric Geometry
2012-05-15 v1
Abstract
We consider some properties of the intersection of deleted digits Cantor sets with their translates. We investigate conditions on the set of digits such that, for any t between zero and the dimension of the deleted digits Cantor set itself, the set of translations such that the intersection has Hausdorff dimension equal to t is dense in the set F of translations such that the intersection is non-empty. We make some simple observations regarding properties of the set F, in particular, we characterize when F is an interval, in terms of conditions on the digit set.
Cite
@article{arxiv.1105.3463,
title = {Intersections of certain deleted digits sets},
author = {Steen Pedersen and Jason Phillips},
journal= {arXiv preprint arXiv:1105.3463},
year = {2012}
}
Comments
15 pages, 5 figures