Geodesic
Attainable forms of intermediate dimensions
Amlan Banaji1 ; Alex Rutar1
1 University of St Andrews, Mathematical Institute
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 939-960 Cet article a éte moissonné depuis la source Journal.fi

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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 $h(\theta)$ to be realized as the intermediate dimensions of a bounded subset of $\mathbb{R}^d$. This condition is a straightforward constraint on the Dini derivatives of $h(\theta)$, which we prove is sharp using a homogeneous Moran set construction.  
DOI : 10.54330/afm.120529
Keywords: Hausdorff dimension, box dimension, intermediate dimensions, Moran set

Amlan Banaji 1 ; Alex Rutar 1

1 University of St Andrews, Mathematical Institute 
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Amlan Banaji; Alex Rutar. Attainable forms of intermediate dimensions. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 939-960. doi: 10.54330/afm.120529

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