Dimensions of the popcorn graph
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866910371885875200 |
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| author | Chen, Haipeng Fraser, Jonathan M. Yu, Han |
| author_facet | Chen, Haipeng Fraser, Jonathan M. Yu, Han |
| contents | 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-Erdős inequality from probability theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_08407 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Dimensions of the popcorn graph Chen, Haipeng Fraser, Jonathan M. Yu, Han Metric Geometry Classical Analysis and ODEs Number Theory 28A80, 11B57 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-Erdős inequality from probability theory. |
| title | Dimensions of the popcorn graph |
| topic | Metric Geometry Classical Analysis and ODEs Number Theory 28A80, 11B57 |
| url | https://arxiv.org/abs/2007.08407 |