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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 language | English |
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Pages (from-to) | 4729-4742 |
Journal | Proceedings of the American Mathematical Society |
Volume | 150 |
Early online date | 18 Aug 2022 |
DOIs | |
Publication status | E-pub ahead of print - 18 Aug 2022 |
Keywords
- Popcorn function
- Thomae function
- Box dimension
- Assouad dimension
- Assouad spectrum
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Dive into the research topics of 'Dimensions of the popcorn graph'. Together they form a unique fingerprint.Projects
- 2 Finished
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New perspectives in the dimension: New perspectives in the dimension theory of fractals
Fraser, J. (PI)
1/09/19 → 31/01/23
Project: Standard
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Fourier analytic techniques: Fourier analytic techniques in geometry and analysis
Fraser, J. (PI) & Falconer, K. J. (CoI)
1/02/18 → 11/06/21
Project: Standard