On universal and periodic \(\beta\)-expansions, and the Hausdorff dimension of the set of all expansions
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Publication:2439815
DOI10.1007/s10474-013-0366-0zbMath1299.11052arXiv1212.1349OpenAlexW2015615479MaRDI QIDQ2439815
Publication date: 17 March 2014
Published in: Acta Mathematica Hungarica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1212.1349
Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Hausdorff and packing measures (28A78) Dimension theory of smooth dynamical systems (37C45)
Related Items
Unique expansions and intersections of Cantor sets, Finite orbits in multivalued maps and Bernoulli convolutions, The Two-Dimensional Density of Bernoulli Convolutions
Cites Work
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- Counting \(\beta \)-expansions and the absolute continuity of Bernoulli convolutions
- Growth rate for beta-expansions
- Developments in non-integer bases
- Universal \(\beta\)-expansions
- Discrete spectra and Pisot numbers
- On the topology of polynomials with bounded integer coefficients
- On the topology of sums in powers of an algebraic number
- Intersections of homogeneous Cantor sets and beta-expansions
- The growth rate and dimension theory of beta-expansions
- Arithmetic Properties of Bernoulli Convolutions
- On Periodic Expansions of Pisot Numbers and Salem Numbers
- Almost Every Number Has a Continuum of b-Expansions
- Combinatorics of linear iterated function systems with overlaps
- Beta-expansions, natural extensions and multiple tilings associated with Pisot units
- Generalised golden ratios over integer alphabets
- Characterization of the unique expansions $1=\sum^{\infty}_{i=1}q^{-n_ i}$ and related problems
- Unique representations of real numbers in non-integer bases
