Diophantine analysis in beta-dynamical systems and Hausdorff dimensions

DOI10.1016/j.aim.2015.12.016zbMath1332.11075OpenAlexW2231444123MaRDI QIDQ908085

Jun Wu, Fan Lü

Publication date: 2 February 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2015.12.016

zbMATH Keywords

Diophantine approximationHausdorff dimensionbeta-dynamical system

Mathematics Subject Classification ID

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

Related Items

APPROXIMATION ORDERS OF A REAL NUMBER IN A FAMILY OF BETA-DYNAMICAL SYSTEMS, Approximation orders of real numbers by \(\beta\)-expansions, On dichotomy law for beta-dynamical system in parameter space, Maximal run-length function for real numbers in beta-dynamical system, Run-length function of the beta-expansion of a fixed real number, Dichotomy law for shrinking target problems in a nonautonomous dynamical system: Cantor series expansion, Approximation orders of the unit in the \(\beta\)-dynamical systems, A Survey on the Dimension Theory in Dynamical Diophantine Approximation, The -transformation with a hole at 0, Quantitative recurrence properties for systems with non-uniform structure, The run-length function of the \(\beta\)-expansion of the unit, APPROXIMATION PROPERTIES OF THE ORBITS UNDER β-TRANSFORMATION, A general principle for Hausdorff measure, Quantitative recurrence properties in the historic set for symbolic systems, Modified shrinking target problems on self-conformal sets, Relative bifurcation sets and the local dimension of univoque bases, Shrinking targets in parametrised families, UNIFORM DIOPHANTINE APPROXIMATION TO CANTOR SERIES EXPANSION

Cites Work

• \(\beta\)-expansions and symbolic dynamics
• A result on the approximation properties of the orbit of 1 under the \(\beta\)-transformation
• Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions
• A mass transference principle and the Duffin-Schaeffer conjecture for Hausdorff measures
• Dimension of countable intersections of some sets arising in expansions in non-integer bases
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Symbolic dynamics for $\beta$-shifts and self-normal numbers
• Dyadic Diophantine approximation and Katok's horseshoe approximation
• \(\beta\)-shifts have unique maximal measure