Nonstandard approximations to Besicovitch sets

Paul Potgieter

Chaos, Solitons & Fractals, 2023, vol. 167, issue C

Abstract: A nonstandard approximation to a Besicovitch set in R2 is constructed. It is shown that this approximation easily yields the correct upper Minkowski dimension in the two-dimensional case through a direct computation. By constructing an approximation to a Besicovitch set in three dimensions, we use a theorem of Guth and Katz to obtain an upper bound on the number of intersections of line segments in nonstandard terms.

Keywords: Nonstandard analysis; Minkowski dimension; Besicovitch set; Guth–Katz theorem (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012152

DOI: 10.1016/j.chaos.2022.113036

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