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

Baker, S. (2014) On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions. Acta Mathematica Hungarica, 142 (1). pp. 95-109. ISSN 1588-2632 doi: 10.1007/s10474-013-0366-0

Abstract/Summary

We study the topology of a set naturally arising from the study of β-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 β-expansions are equal and explicitly calculable.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/46859
Identification Number/DOI	10.1007/s10474-013-0366-0
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
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