Hausdorff dimension of some sets arising by the run-length function of \(\beta\)-expansions

DOI10.1016/j.jmaa.2017.06.001zbMath1405.11098OpenAlexW2622783475MaRDI QIDQ2013118

Jia Liu, Mei-Ying Lü

Publication date: 3 August 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.06.001

zbMATH Keywords

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

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80)

Related Items (5)

On the exceptional sets in Erdös–Rényi limit theorem of β-expansion ⋮ Diophantine approximation and run-length function on \({\beta}\)-expansions ⋮ Maximal run-length function with constraints: a generalization of the Erdős-Rényi limit theorem and the exceptional sets ⋮ EXCEPTIONAL SETS RELATED TO THE RUN-LENGTH FUNCTION OF BETA-EXPANSIONS ⋮ RUN-LENGTH FUNCTION FOR REAL NUMBERS IN β-EXPANSIONS

Cites Work

• Distribution of full cylinders and the Diophantine properties of the orbits in \(\beta\)-expansions
• On exceptional sets in Erdős-Rényi limit theorem revisited
• On exceptional sets in Erdős-Rényi limit theorem
• Egoroff's theorem and maximal run length
• On a new law of large numbers
• On the maximal length of consecutive zero digits of β-expansions
• Hausdorff dimension of the maximal run-length in dyadic expansion
• On the lengths of basic intervals in beta expansions
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers

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