On the escape rate of unique beta-expansions
Dynamical Systems
2016-11-22 v2 Number Theory
Abstract
Let . It is well-known that the set of points in having unique -expansion, in other words, those points whose orbits under greedy -transformation escape a hole depending on , is of zero Lebesgue measure. The corresponding escape rate is investigated in this paper. A formula which links the Hausdorff dimension of univoque set and escape rate is established in this study. Then we also proved that such rate forms a devil's staircase function with respect to .
Keywords
Cite
@article{arxiv.1510.01117,
title = {On the escape rate of unique beta-expansions},
author = {Jung-Chao Ban and Chih-Hung Chang and Bing Li},
journal= {arXiv preprint arXiv:1510.01117},
year = {2016}
}