Slicing the Sierpi\'nski gasket
Dynamical Systems
2013-01-31 v1
Abstract
We investigate the dimension of intersections of the Sierpi\'nski gasket with lines. Our first main result describes a countable, dense set of angles that are exceptional for Marstrand's theorem. We then provide a multifractal analysis for the set of points in the projection for which the associated slice has a prescribed dimension.
Cite
@article{arxiv.1301.7077,
title = {Slicing the Sierpi\'nski gasket},
author = {Balázs Bárány and Andrew Ferguson and Károly Simon},
journal= {arXiv preprint arXiv:1301.7077},
year = {2013}
}
Comments
19 pages, 4 figures