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Nonstandard approximations to Besicovitch sets

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  • Potgieter, Paul

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.

Suggested Citation

  • Potgieter, Paul, 2023. "Nonstandard approximations to Besicovitch sets," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012152
    DOI: 10.1016/j.chaos.2022.113036
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