Attainable forms of intermediate dimensions

Amlan Banaji; Alex Rutar

doi:10.54330/afm.120529

Attainable forms of intermediate dimensions

Amlan Banaji, Alex Rutar

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The intermediate dimensions are a family of dimensions which interpolate between the Hausdorff and box dimensions of sets. We prove a necessary and sufficient condition for a given function h(θ) to be realized as the intermediate dimensions of a bounded subset of R^d. This condition is a straightforward constraint on the Dini derivatives of h(θ), which we prove is sharp using a homogeneous Moran set construction.

Original language	English
Pages (from-to)	939-960
Journal	Annales Academiae Scientiarum Fennicae-Mathematica
Volume	47
Issue number	2
DOIs	https://doi.org/10.54330/afm.120529
Publication status	Published - 4 Jul 2022

Keywords

Hausdorff dimension
Box dimension
Intermediate dimensions
Moran set

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10.54330/afm.120529Licence: CC BY-NC

Banaji_2022_AASFM_Attainableforms_CC
Copyright (c) 2022 Annales Fennici Mathematici. Open Access. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Final published version, 655 KBLicence: CC BY-NC

https://arxiv.org/abs/2111.14678Licence: Other

Assouad-type dimensions and the local geometry of fractal sets
Rutar, A. (Author), Falconer, K. J. (Supervisor) & Fraser, J. M. (Supervisor), 3 Dec 2024
Student thesis: Doctoral Thesis (PhD)

Cite this

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KW - Intermediate dimensions

KW - Moran set

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Attainable forms of intermediate dimensions

Abstract

Keywords

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Student theses

Assouad-type dimensions and the local geometry of fractal sets

Cite this