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arXiv · 2502.04149

Rotational beta expansions and Schmidt games

Hajime Kaneko·Jonathan Caalim·Nathaniel Nollen
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Abstract

We consider rotational beta expansions in dimensions 1, 2 and 4 and view them as expansions on real numbers, complex numbers, and quaternions, respectively. We give sufficient conditions on the parameters $\alpha, \beta \in (0,1)$ so that particular cylinder sets arising from the expansions are winning or losing Schmidt $(\alpha,\beta)$-game.

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Hajime Kaneko, Jonathan Caalim, Nathaniel Nollen. 2025-02-06. Rotational beta expansions and Schmidt games. https://arxiv.org/abs/2502.04149

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