Beatty multiple shifts are defined and their Hausdorff and Minkowski dimensions are computed explicitly for five of six parameter regions, leaving one region open.
Brunet, Dimensions of self-affine sponges invariant under the action of mul- tiplicative integers, Ergodic Theory and Dynamical Systems (2021), 1–43
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Hausdorff dimensions of Beatty multiple shifts
Beatty multiple shifts are defined and their Hausdorff and Minkowski dimensions are computed explicitly for five of six parameter regions, leaving one region open.