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arXiv:1212.1349 [math.DS]AbstractReferencesReviewsResources

On universal and periodic $β$-expansions, and the Hausdorff dimension of the set of all expansions

Simon Baker

Published 2012-12-06, updated 2013-05-28Version 2

In this paper we study the topology of a set naturally arising from the study of $\beta$-expansions. After proving several elementary results for this set we study the case when our base is Pisot. In this case we give necessary and sufficient conditions for this set to be finite. This finiteness property will allow us to generalise a theorem due to Schmidt and will provide the motivation for sufficient conditions under which the growth rate and Hausdorff dimension of the set of $\beta$-expansions are equal and explicitly calculable.

Journal: Acta Mathematica Hungarica: Volume 142, Issue 1 (2014), Page 95-109
Categories: math.DS, math.NT
Subjects: 37A45, 37C45
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