ON SHRINKING TARGETS FOR ℤ m ACTIONS ON TORI

DOI10.1112/S0025579310001130zbMath1227.11095arXiv0807.3863OpenAlexW2963591593MaRDI QIDQ3584586

Simon Kristensen, Stephen Harrap, Sanju L. Velani, Yann Bugeaud

Publication date: 30 August 2010

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.3863

zbMATH Keywords

diophantine approximation

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Metric theory (11J83) Diophantine approximation in probabilistic number theory (11K60) Rotation numbers and vectors (37E45)

Related Items

A temporal central limit theorem for real-valued cocycles over rotations, Doubly metric theory and simultaneous shrinking target problem in Cantor series expansion, Modified shrinking target problem in beta dynamical systems, Dynamics of Ostrowski skew-product: 1. Limit laws and Hausdorff dimensions, Distribution of full cylinders and the Diophantine properties of the orbits in \(\beta\)-expansions, A NOTE ON BADLY APPROXIMABLE LINEAR FORMS ON MANIFOLDS, SIMULTANEOUS DYNAMICAL DIOPHANTINE APPROXIMATION IN BETA EXPANSIONS, A Survey on the Dimension Theory in Dynamical Diophantine Approximation, A solution to a problem of Cassels and Diophantine properties of cubic numbers, Badly approximable systems of affine forms and incompressibility on fractals, A NOTE ON WEIGHTED BADLY APPROXIMABLE LINEAR FORMS, Badly approximable points in twisted Diophantine approximation and Hausdorff dimension, Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions, Kurzweil type metrical Diophantine properties in the field of formal Laurent series, Diophantine approximation by orbits of expanding Markov maps, Inhomogeneous Diophantine approximation in the coprime setting, Recurrence to Shrinking Targets on Typical Self-Affine Fractals, Dynamical Diophantine approximation of beta expansions of formal Laurent series

Cites Work

• Unnamed Item
• Metric Diophantine approximation and `absolutely friendly' measures
• Badly approximable vectors on fractals
• On circle rotations and the shrinking target properties
• The ergodic theory of shrinking targets
• A mass transference principle and the Duffin-Schaeffer conjecture for Hausdorff measures
• Diophantine approximation and badly approximable sets
• On simultaneous inhomogeneous Diophantine approximation
• MIXING IN THE ABSENCE OF THE SHRINKING TARGET PROPERTY
• The shrinking target property of irrational rotations
• Numbers contravening a condition in density modulo 1
• A NOTE ON INHOMOGENEOUS DIOPHANTINE APPROXIMATION
• A NOTE ON INHOMOGENEOUS DIOPHANTINE APPROXIMATION WITH A GENERAL ERROR FUNCTION