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arXiv · 2006.16130

Hausdorff distance of univoque sets

Yi Cai·Vilmos Komornik
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Abstract

Expansions in non-integer bases have been investigated abundantly since their introduction by Rényi. It was discovered by Erdős et al. that the sets of numbers with a unique expansion have a much more complex structure than in the integer base case. The present paper is devoted to the continuity properties of these maps with respect to the Hausdorff metric.

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Yi Cai, Vilmos Komornik. 2020-06-29. Hausdorff distance of univoque sets. https://arxiv.org/abs/2006.16130

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