Dimensions of the popcorn graph
- 18 August 2022
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 150 (11), 4729-4742
- https://doi.org/10.1090/proc/15729
Abstract
The `popcorn function' is a well-known and important example in real analysis with many interesting features. We prove that the box dimension of the graph of the popcorn function is 4/3, as well as computing the Assouad dimension and Assouad spectrum. The main ingredients include Duffin-Schaeffer type estimates from Diophantine approximation and the Chung-Erdos inequality from probability theory.Keywords
Funding Information
- China Scholarship Council (201906150102, 11601161, 11771153, 11871227, EP/R015104/1, RPG-2019-034, 803711)
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