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Dimensions of the popcorn graph.

Authors :
Chen, Haipeng
Fraser, Jonathan M.
Yu, Han
Source :
Proceedings of the American Mathematical Society. Nov2022, Vol. 150 Issue 11, p4729-4742. 14p.
Publication Year :
2022

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-Erdős inequality from probability theory. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00029939
Volume :
150
Issue :
11
Database :
Academic Search Index
Journal :
Proceedings of the American Mathematical Society
Publication Type :
Academic Journal
Accession number :
159358907
Full Text :
https://doi.org/10.1090/proc/15729