Hausdorff dimension of some sets in the theory of continued beta-fractions and its generalized continued fractions

DOI10.1016/j.jmaa.2024.128120OpenAlexW4391069551WikidataQ129621497 ScholiaQ129621497MaRDI QIDQ6191122

Ziheng Song

Publication date: 6 March 2024

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.2024.128120

zbMATH Keywords

Hausdorff dimension\(\beta\)-expansiongeneralized continued fractionscontinued \(\beta\)-fractions

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Continued fractions (11A55) Metric theory of continued fractions (11K50)

Cites Work

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• Continued fractions and numeration in the Fibonacci base
• Asymptotic behavior of beta-integers
• \(\beta\)-expansions and symbolic dynamics
• Metric theorems for continued \(\beta\)-fractions
• Beta-expansion and continued fraction expansion
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Good’s theorem for Hurwitz continued fractions
• Beta-integers as natural counting systems for quasicrystals
• Symbolic dynamics for $\beta$-shifts and self-normal numbers
• Limit theorems related to beta-expansion and continued fraction expansion