The Shrinking Target Problem for Matrix Transformations of Tori

DOI10.1112/S0024610799007681zbMath0987.37008OpenAlexW2015841534WikidataQ128523869 ScholiaQ128523869MaRDI QIDQ4487495

Richard M. Hill, Sanju L. Velani

Publication date: 22 June 2000

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0024610799007681

zbMATH Keywords

Hausdorff dimensionergodic theorymetric diophantine approximation

Mathematics Subject Classification ID

Related Items (18)

Dimensions of random covering sets in Riemann manifolds ⋮ The shrinking target problem for matrix transformations of tori: revisiting the standard problem ⋮ ON THE HAUSDORFF MEASURE OF SHRINKING TARGET SETS ON SELF‐CONFORMAL SETS ⋮ Shrinking target problems for beta-dynamical system ⋮ Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps ⋮ Mass transference principle for limsup sets generated by rectangles ⋮ Quantitative recurrence and the shrinking target problem for overlapping iterated function systems ⋮ Recurrence in \(\beta \)-expansion over formal Laurent series ⋮ A Survey on the Dimension Theory in Dynamical Diophantine Approximation ⋮ Quantitative recurrence properties for beta-dynamical system ⋮ Uniform recurrence properties for beta-transformation ⋮ Mass transference principle from rectangles to rectangles in Diophantine approximation ⋮ Quantitative recurrence properties for systems with non-uniform structure ⋮ Diophantine approximation by orbits of expanding Markov maps ⋮ Recurrence to Shrinking Targets on Typical Self-Affine Fractals ⋮ A DICHOTOMY LAW FOR THE DIOPHANTINE PROPERTIES IN ‐DYNAMICAL SYSTEMS ⋮ Quantitative recurrence properties in the historic set for symbolic systems ⋮ Moving recurrent properties for the doubling map on the unit interval

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