English

Hausdorff distance of univoque sets

Number Theory 2020-06-30 v1

Abstract

Expansions in non-integer bases have been investigated abundantly since their introduction by R\'enyi. It was discovered by Erd\H{o}s 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.

Keywords

Cite

@article{arxiv.2006.16130,
  title  = {Hausdorff distance of univoque sets},
  author = {Yi Cai and Vilmos Komornik},
  journal= {arXiv preprint arXiv:2006.16130},
  year   = {2020}
}