Distribution of full cylinders and the Diophantine properties of the orbits in \(\beta\)-expansions

DOI10.4171/JFG/6zbMath1309.11062OpenAlexW1997230923MaRDI QIDQ407405

Publication date: 1 September 2014

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jfg/6

zbMATH Keywords

Hausdorff dimension \(\beta\)-expansions Diophantine properties full cylinders

Mathematics Subject Classification ID

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

Related Items

On the intersection of dynamical covering sets with fractals, The points with dense orbit under the \(\beta\)-expansions of different bases, On the exceptional sets in Erdös–Rényi limit theorem of β-expansion, SHRINKING TARGETS FOR NONAUTONOMOUS DYNAMICAL SYSTEMS CORRESPONDING TO CANTOR SERIES EXPANSIONS, HIGHER-DIMENSIONAL SHRINKING TARGET PROBLEM FOR BETA DYNAMICAL SYSTEMS, The shrinking target problem for matrix transformations of tori: revisiting the standard problem, Diophantine approximation and run-length function on \({\beta}\)-expansions, SHRINKING TARGET PROBLEM FOR RANDOM IFS, APPROXIMATION ORDERS OF A REAL NUMBER IN A FAMILY OF BETA-DYNAMICAL SYSTEMS, Approximation orders of real numbers by \(\beta\)-expansions, Maximal run-length function for real numbers in beta-dynamical system, TWO-DIMENSIONAL SHRINKING TARGET PROBLEM IN BETA-DYNAMICAL SYSTEMS, Path-dependent shrinking target problems in beta-dynamical systems, ON THE LONGEST BLOCK FUNCTION IN CONTINUED FRACTIONS, Dichotomy law for shrinking target problems in a nonautonomous dynamical system: Cantor series expansion, A Survey on the Dimension Theory in Dynamical Diophantine Approximation, Beta-expansion and continued fraction expansion of real numbers, Dimensions of recurrent sets in \(\beta\)-symbolic dynamics, A result on the maximal length of consecutive 0 digits in β-expansions, Diophantine approximation of the orbits in topological dynamical systems, The -transformation with a hole at 0, Uniform recurrence properties for beta-transformation, The topological property of the irregular sets on the lengths of basic intervals in beta-expansions, On the distal and asymptotic sets for \(\beta\)-transformations, Distributions of full and non-full words in beta-expansions, Hausdorff dimension of some sets arising by the run-length function of \(\beta\)-expansions, Best approximation of orbits in iterated function systems, A dynamical dimension transference principle for dynamical Diophantine approximation, On the maximal length of consecutive zero digits of β-expansions, Expansions in multiple bases, Limit theorems related to beta-expansion and continued fraction expansion, 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, THE EXCEPTIONAL SETS ON THE RUN-LENGTH FUNCTION OF β-EXPANSIONS, A DICHOTOMY LAW FOR THE DIOPHANTINE PROPERTIES IN ‐DYNAMICAL SYSTEMS, Inhomogeneous potentials, Hausdorff dimension and shrinking targets, Hausdorff dimension of frequency sets of univoque sequences, Modified shrinking target problems on self-conformal sets, Shrinking targets in parametrised families, Inhomogeneous and simultaneous Diophantine approximation in beta dynamical systems, Hausdorff dimension of frequency sets in beta-expansions, RUN-LENGTH FUNCTION FOR REAL NUMBERS IN β-EXPANSIONS, UNIFORM DIOPHANTINE APPROXIMATION TO CANTOR SERIES EXPANSION

Cites Work