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The growth rate and dimension theory of beta-expansions

Tom 219 / 2012

Simon Baker Fundamenta Mathematicae 219 (2012), 271-285 MSC: 37A45, 37C45. DOI: 10.4064/fm219-3-6

Streszczenie

In a recent paper of Feng and Sidorov they show that for $\beta\in(1,(1+\sqrt{5})/2)$ the set of $\beta$-expansions grows exponentially for every $x\in(0,1/(\beta-1))$. In this paper we study this growth rate further. We also consider the set of $\beta$-expansions from a dimension theory perspective.

Autorzy

  • Simon BakerSchool of Mathematics
    The University of Manchester
    Oxford Road
    Manchester, M13 9PL, UK
    e-mail

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