On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansionsBaker, 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
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1007/s10474-013-0366-0 Abstract/SummaryWe 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.
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