Intermediate dimensions under self-affine codings

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.