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Rectangular shrinking targets for actions on tori: well and badly approximable systems

Volume 216 / 2024

V. Beresnevich, S. Datta, A. Ghosh, B. Ward Acta Arithmetica 216 (2024), 349-363 MSC: Primary 11J83; Secondary 11K60 DOI: 10.4064/aa231108-27-8 Published online: 22 November 2024

Abstract

We investigate the shrinking target property for irrational rotations. This was first studied by Kurzweil (1951) and has received considerable interest as of late. Using a new approach, we generalize results of Kim (2007) and Shapira (2013) by proving a weighted effective analogue of the shrinking target property. Furthermore, our results are established in the much wider S-arithmetic setting.

Authors

  • V. BeresnevichDepartment of Mathematics
    University of York
    Heslington, York, YO10 5DD, UK
    e-mail
  • S. DattaDepartment of Mathematics
    University of York
    Heslington, York, YO10 5DD, UK
    e-mail
    e-mail
  • A. GhoshSchool of Mathematics
    Tata Institute of Fundamental Research
    Mumbai 400005, India
    e-mail
  • B. WardLa Trobe University Bendigo Campus
    Bendigo, Victoria 3552, Australia
    e-mail

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