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.
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}
}