10198452-10.4171-jfg-135-print.pdf (1.99 MB)
Dimensions of popcorn-like pyramid sets
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–Erdos inequality from probability theory, higherdimensional 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.
Funding
Leverhulme Trust Research Project Grant (RPG-2019-034)
NSFC (No. 11871227)
Shenzhen Science and Technology Program (Grant No. RCBS20210706092219049)
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Fractal GeometryVolume
10Issue
1Pages
151-168Publisher
EMS PressVersion
- VoR (Version of Record)
Rights holder
© European Mathematical SocietyPublisher statement
This is an Open Access Article. It is published by EMS Press under the Creative Commons Attribution 4.0 International Licence (CC BY). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/Acceptance date
2023-02-25Publication date
2023-04-10Copyright date
2023ISSN
2308-1309eISSN
2308-1317Publisher version
Language
- en