Dimensions of popcorn-like pyramid sets
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This article concerns the dimension theory of the graphs of a family of functions which include the well-known 'popcorn function' and its pyramid-like higher-dimensional analogues. We calculate the box and Assouad dimensions of these graphs, as well as the intermediate dimensions, which are a family of dimensions interpolating between Hausdorff and box dimension. As tools in the proofs, we use the Chung–Erdős inequality from probability theory, higher-dimensional Duffin–Schaeffer type estimates from Diophantine approximation, and a bound for Euler's totient function. As applications we obtain bounds on the box dimension of fractional Brownian images of the graphs, and on the Hölder distortion between different graphs.
Banaji , A & Chen , H 2023 , ' Dimensions of popcorn-like pyramid sets ' , Journal of Fractal Geometry , vol. 10 , no. 1 , pp. 151-168 . https://doi.org/10.4171/jfg/135
Journal of Fractal Geometry
Copyright © 2023 European Mathematical Society. Published by EMS Press. This work is licensed under a CC BY 4.0 license.
DescriptionAB was financially supported by a Leverhulme Trust Research Project Grant (RPG-2019-034). HC was supported by NSFC (No. 11871227) and Shenzhen Science and Technology Program (Grant No. RCBS20210706092219049).
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