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.
Original language | English |
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Publisher | arXiv |
Number of pages | 14 |
DOIs | |
Publication status | Submitted - 22 Feb 2021 |
Keywords
- Box dimension
- Method of types
- Self-affine sponge
- Ledrappier-Young formula