Rectangular shrinking targets for $\mathbb{Z}^m$ actions on tori: well and badly approximable systems
Dynamical Systems
2025-04-08 v1 Number Theory
Abstract
In this paper we investigate the shrinking target property for irrational rotations. This was first studied by Kurzweil (1951) and has received considerable interest 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 -arithmetic setting.
Cite
@article{arxiv.2307.10122,
title = {Rectangular shrinking targets for $\mathbb{Z}^m$ actions on tori: well and badly approximable systems},
author = {Victor Beresnevich and Shreyasi Datta and Anish Ghosh and Benjamin Ward},
journal= {arXiv preprint arXiv:2307.10122},
year = {2025}
}