Dimensions of the popcorn graph
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- by Haipeng Chen, Jonathan M. Fraser and Han Yu PDF
- Proc. Amer. Math. Soc. 150 (2022), 4729-4742 Request permission
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.References
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Additional Information
- Haipeng Chen
- Affiliation: College of Big Data and Internet, Shenzhen Technology University, Shenzhen, People’s Republic of China
- MR Author ID: 1215430
- Email: hpchen0703@foxmail.com
- Jonathan M. Fraser
- Affiliation: Mathematical Institute, University of St Andrews, United Kingdom
- MR Author ID: 946983
- ORCID: 0000-0002-8066-9120
- Email: jmf32@st-andrews.ac.uk
- Han Yu
- Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, United Kingdom
- MR Author ID: 1223262
- Email: hy351@math.cam.ac.uk
- Received by editor(s): August 4, 2020
- Received by editor(s) in revised form: May 14, 2021
- Published electronically: August 18, 2022
- Additional Notes: The first author was funded by China Scholarship Council (File No. 201906150102) and NSFC (No. 11601161, 11771153 and 11871227) and Shenzhen Science and Technology Program (Grant No. RCBS20210706092219049) and is thankful for the excellent atmosphere for research provided by the University of St Andrews. The second author was funded by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). The third author was funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 803711), and indirectly by Corpus Christi College, Cambridge
- Communicated by: Katrin Gelfert
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 4729-4742
- MSC (2020): Primary 28A80; Secondary 11B57
- DOI: https://doi.org/10.1090/proc/15729