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math.NTOct 16, 2007
42
citations (OpenAlex)
authors
  • Claudio Baiocchi
  • Vilmos Komornik
arXiv abstractPDF
paper

Greedy and quasi-greedy expansions in non-integer bases

arXiv:0710.3001

Abstract

We generalize several theorems of Rényi, Parry, Daróczy and Kátai by characterizing the greedy and quasi-greedy expansions in non-integer bases.

10 pages

Cited by in corpus (17)

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  • Hausdorff dimension of univoque sets and Devil's staircase
  • Relative bifurcation sets and the local dimension of univoque bases
  • Entropy, topological transitivity, and dimensional properties of unique q-expansions
  • Bifurcation sets arising from non-integer base expansions
  • Digit frequencies and self-affine sets with non-empty interior
  • Univoque bases and Hausdorff dimension
  • On the specification property and synchronisation of unique q-expansions
  • On the bifurcation set of unique expansions
  • Critical base for the unique codings of fat Sierpinski gasket
  • Univoque bases of real numbers: local dimension, Devil's staircase and isolated points
  • Expansions in multiple bases
  • Univoque graphs and multiple expansions
  • Smallest bases of expansions with multiple digits
  • Typical points of univoque sets
  • Bases in which some numbers have exactly two expansions
  • On the number of unique expansions in non-integer bases
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