Dimensions of the popcorn graph

Haipeng Chen, Jonathan Fraser, Han Yu

Research output: Contribution to journalArticlepeer-review

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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.
Original languageEnglish
Pages (from-to)4729-4742
JournalProceedings of the American Mathematical Society
Volume150
Early online date18 Aug 2022
DOIs
Publication statusE-pub ahead of print - 18 Aug 2022

Keywords

  • Popcorn function
  • Thomae function
  • Box dimension
  • Assouad dimension
  • Assouad spectrum

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