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Calculating box dimension with the method of types

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Abstract

This paper presents a general procedure based on using the method of types to calculate the box dimension of sets. The approach unifies and simplifies multiple box counting arguments. In particular, we use it to generalize the formula for the box dimension of self-affine carpets of Gatzouras-Lalley and of Bara\'nski type to their higher dimensional sponge analogues. In addition to a closed form, we also obtain a variational formula which resembles the Ledrappier-Young formula for Hausdorff dimension.
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Original languageEnglish
JournalArXiv e-prints
Publication statusSubmitted - 22 Feb 2021

    Research areas

  • box dimension, method of types, self-affine sponge, Ledrappier-Young formula

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