Bounding the Dimension of Points on a Line

Neil Lutz; D. M. Stull

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arXiv · 1612.00143

Bounding the Dimension of Points on a Line

Neil Lutz·D. M. Stull

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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.

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BibTeX RIS

Neil Lutz, D. M. Stull. 2016-12-01. Bounding the Dimension of Points on a Line. https://arxiv.org/abs/1612.00143

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