A DICHOTOMY LAW FOR THE DIOPHANTINE PROPERTIES IN ‐DYNAMICAL SYSTEMS

DOI10.1112/S0025579316000085zbMath1396.11101arXiv1604.00747MaRDI QIDQ2827921

Michael Coons, Mumtaz Hussain, Bao-Wei Wang

Publication date: 21 October 2016

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.00747

zbMATH Keywords

Hausdorff measure\(\beta\)-expansionsshrinking target problems

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Metric theory (11J83) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Diophantine approximation in probabilistic number theory (11K60)

Related Items (7)

MEAN LI–YORKE CHAOTIC SET WITH FULL HAUSDORFF DIMENSION FOR CONTINUED FRACTIONS ⋮ HIGHER-DIMENSIONAL SHRINKING TARGET PROBLEM FOR BETA DYNAMICAL SYSTEMS ⋮ TWO-DIMENSIONAL SHRINKING TARGET PROBLEM IN BETA-DYNAMICAL SYSTEMS ⋮ SIMULTANEOUS DYNAMICAL DIOPHANTINE APPROXIMATION IN BETA EXPANSIONS ⋮ On the distal and asymptotic sets for \(\beta\)-transformations ⋮ A general principle for Hausdorff measure ⋮ Inhomogeneous and simultaneous Diophantine approximation in beta dynamical systems

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