Bounding the Dimension of Points on a Line
Computational Complexity
2017-04-07 v3 Classical Analysis and ODEs
Abstract
We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff dimension of the point (x, ax+b), given real numbers a, b, and x. We apply our main theorem to a problem in fractal geometry, giving an improved lower bound on the (classical) Hausdorff dimension of generalized sets of Furstenberg type.
Keywords
Cite
@article{arxiv.1612.00143,
title = {Bounding the Dimension of Points on a Line},
author = {Neil Lutz and D. M. Stull},
journal= {arXiv preprint arXiv:1612.00143},
year = {2017}
}