Dimensions of the popcorn graph
Metric Geometry
2024-03-20 v2 Classical Analysis and ODEs
Number Theory
Abstract
The 'popcorn function' isThe `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-Erd\H{o}s inequality from probability theory.
Keywords
Cite
@article{arxiv.2007.08407,
title = {Dimensions of the popcorn graph},
author = {Haipeng Chen and Jonathan M. Fraser and Han Yu},
journal= {arXiv preprint arXiv:2007.08407},
year = {2024}
}
Comments
13 pages, 2 figures