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Intermediate dimensions under self-affine codings.
- Source :
- Mathematische Zeitschrift; May2024, Vol. 307 Issue 1, p1-29, 29p
- Publication Year :
- 2024
-
Abstract
- Intermediate dimensions were recently introduced by Falconer et al. (Math Z 296:813–830, 2020) to interpolate between the Hausdorff and box-counting dimensions. In this paper, we show that for every subset E of the symbolic space, the intermediate dimensions of the projections of E under typical self-affine coding maps are constant and given by formulas in terms of capacities. Moreover, we extend the results to the generalized intermediate dimensions introduced by Banaji (Monatsh Math 202: 465–506, 2023) in several settings, including the orthogonal projections in Euclidean spaces and the images of fractional Brownian motions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255874
- Volume :
- 307
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Mathematische Zeitschrift
- Publication Type :
- Academic Journal
- Accession number :
- 177057930
- Full Text :
- https://doi.org/10.1007/s00209-024-03490-z