The run-length function of the \(\beta\)-expansion of the unit

DOI10.1016/J.JNT.2017.01.015zbMath1426.11078OpenAlexW2591781150MaRDI QIDQ529461

Yuan-Hong Chen, Chun-Yun Cao

Publication date: 18 May 2017

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2017.01.015

zbMATH Keywords

Hausdorff dimension\(\beta\)-expansionrun-length function

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Radix representation; digital problems (11A63)

Related Items (5)

Diophantine approximation and run-length function on \({\beta}\)-expansions ⋮ Run-length function of the beta-expansion of a fixed real number ⋮ EXCEPTIONAL SETS RELATED TO THE RUN-LENGTH FUNCTION OF BETA-EXPANSIONS ⋮ HAUSDORFF DIMENSION OF THE EXCEPTIONAL SETS CONCERNING THE RUN-LENGTH FUNCTION OF BETA-EXPANSION ⋮ RUN-LENGTH FUNCTION FOR REAL NUMBERS IN β-EXPANSIONS

Cites Work

• Unnamed Item
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• Quantitative recurrence properties for beta-dynamical system
• Diophantine analysis in beta-dynamical systems and Hausdorff dimensions
• \(\beta\)-expansions and symbolic dynamics
• Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions
• On the lengths of basic intervals in beta expansions
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Symbolic dynamics for $\beta$-shifts and self-normal numbers
• On a problem of Tamas Varga
• Characterization of the unique expansions $1=\sum^{\infty}_{i=1}q^{-n_ i}$ and related problems

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