On shrinking targets and self-returning points
(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:
https://lup.lub.lu.se/record/3b94a5d3-d654-4a47-b2cf-cfe62782bf01
- author
- Kirsebom, Maxim ; Kunde, Philipp and Persson, Tomas LU
- organization
- publishing date
- 2023
- 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}}, }