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Dimensions of popcorn-like pyramid sets

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journal contribution
posted on 2023-08-11, 13:40 authored by Amlan BanajiAmlan Banaji, Haipeng Chen

This article concerns the dimension theory of the graphs of a family of functions which include the well-known ‘popcorn function’ and its pyramid-like higher-dimensional analogues. We calculate the box and Assouad dimensions of these graphs, as well as the intermediate dimensions, which are a family of dimensions interpolating between Hausdorff and box dimension. As tools in the proofs, we use the Chung–Erdos inequality from probability theory, higherdimensional Duffin–Schaeffer type estimates from Diophantine approximation, and a bound for Euler’s totient function. As applications we obtain bounds on the box dimension of fractional Brownian images of the graphs, and on the Hölder distortion between different graphs.

Funding

Leverhulme Trust Research Project Grant (RPG-2019-034)

NSFC (No. 11871227)

Shenzhen Science and Technology Program (Grant No. RCBS20210706092219049)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Fractal Geometry

Volume

10

Issue

1

Pages

151-168

Publisher

EMS Press

Version

  • VoR (Version of Record)

Rights holder

© European Mathematical Society

Publisher statement

This is an Open Access Article. It is published by EMS Press under the Creative Commons Attribution 4.0 International Licence (CC BY). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/

Acceptance date

2023-02-25

Publication date

2023-04-10

Copyright date

2023

ISSN

2308-1309

eISSN

2308-1317

Language

  • en

Depositor

Amlan Banaji. Deposit date: 12 April 2023

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