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arXiv · 2007.08407

Dimensions of the popcorn graph

Haipeng Chen·Jonathan M. Fraser·Han Yu
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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.

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Haipeng Chen, Jonathan M. Fraser, Han Yu. 2020-07-16. Dimensions of the popcorn graph. https://arxiv.org/abs/2007.08407

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