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Hausdorff dimension of recurrence sets

Hu, Zhang Nan and Persson, Tomas LU orcid (2024) In Nonlinearity 37(5).
Abstract

We consider linear mappings on the 2-dimensional torus, defined by T ( x ) = A x ( mod 1 ) , where A is an invertible 2 × 2 integer matrix, with no eigenvalues on the unit circle. In the case det A = ± 1 , we give a formula for the Hausdorff dimension of the set { x ∈ T 2 : d ( T n ( x ) , x ) < e − α n for infinitely many n } .

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Hausdorff dimension, linear maps, recurrence
in
Nonlinearity
volume
37
issue
5
article number
055010
publisher
IOP Publishing
external identifiers
  • scopus:85189357297
ISSN
0951-7715
DOI
10.1088/1361-6544/ad3597
language
English
LU publication?
yes
id
04d4fab2-d53b-4e4a-b9ef-f5558577ae03
date added to LUP
2024-04-22 14:35:45
date last changed
2025-04-04 15:28:10
@article{04d4fab2-d53b-4e4a-b9ef-f5558577ae03,
  abstract     = {{<p>We consider linear mappings on the 2-dimensional torus, defined by T ( x ) = A x ( mod 1 ) , where A is an invertible 2 × 2 integer matrix, with no eigenvalues on the unit circle. In the case det A = ± 1 , we give a formula for the Hausdorff dimension of the set { x ∈ T 2 : d ( T n ( x ) , x ) &lt; e − α n for infinitely many n } .</p>}},
  author       = {{Hu, Zhang Nan and Persson, Tomas}},
  issn         = {{0951-7715}},
  keywords     = {{Hausdorff dimension; linear maps; recurrence}},
  language     = {{eng}},
  month        = {{05}},
  number       = {{5}},
  publisher    = {{IOP Publishing}},
  series       = {{Nonlinearity}},
  title        = {{Hausdorff dimension of recurrence sets}},
  url          = {{http://dx.doi.org/10.1088/1361-6544/ad3597}},
  doi          = {{10.1088/1361-6544/ad3597}},
  volume       = {{37}},
  year         = {{2024}},
}