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Corpus ID: 211817963

On shrinking targets and self-returning points

@article{Kirsebom2020OnST,
title={On shrinking targets and self-returning points},
author={M. Kirsebom and P. Kunde and T. Persson},
journal={arXiv: Dynamical Systems},
year={2020}
}

We consider the set $\mathcal{R}_\mathrm{io}$ of points returning infinitely many times to a sequence of shrinking targets around themselves. Under additional assumptions we improve Boshernitzan's pioneering result on the speed of recurrence. In the case of the doubling map as well as some linear maps on the $d$ dimensional torus, we even obtain a dichotomy condition for $\mathcal{R}_\mathrm{io}$ to have measure zero or one. Moreover, we study the set of points eventually always returning and… CONTINUE READING