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On shrinking targets and self-returning points

Kirsebom, Maxim ; Kunde, Philipp and Persson, Tomas LU orcid (2023) In Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 24(3). p.1499-1535
Abstract

We consider the set Rio 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 for some linear maps on the d-dimensional torus, we even obtain a dichotomy condition for Rio to have measure-zero or one. Moreover, we study the set of points eventually always returning and prove an analogue of Boshernitzan’s result in similar generality.

Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
volume
24
issue
3
pages
37 pages
publisher
Scuola Normale Superiore
external identifiers
  • scopus:85174141477
ISSN
0391-173X
DOI
10.2422/2036-2145.202110_004
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2023 Scuola Normale Superiore. All rights reserved.
id
3b94a5d3-d654-4a47-b2cf-cfe62782bf01
date added to LUP
2023-12-18 15:24:00
date last changed
2023-12-18 15:26:23
@article{3b94a5d3-d654-4a47-b2cf-cfe62782bf01,
  abstract     = {{<p>We consider the set R<sub>io</sub> 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 for some linear maps on the d-dimensional torus, we even obtain a dichotomy condition for R<sub>io</sub> to have measure-zero or one. Moreover, we study the set of points eventually always returning and prove an analogue of Boshernitzan’s result in similar generality.</p>}},
  author       = {{Kirsebom, Maxim and Kunde, Philipp and Persson, Tomas}},
  issn         = {{0391-173X}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{1499--1535}},
  publisher    = {{Scuola Normale Superiore}},
  series       = {{Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}},
  title        = {{On shrinking targets and self-returning points}},
  url          = {{http://dx.doi.org/10.2422/2036-2145.202110_004}},
  doi          = {{10.2422/2036-2145.202110_004}},
  volume       = {{24}},
  year         = {{2023}},
}