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Dyadic Diophantine Approximation and Katok's Horseshoe Approximation

Persson, Tomas LU orcid and Schmeling, Jörg LU (2008) In Acta Arithmetica 132(3). p.205-230
Abstract
We consider approximations of real numbers by rational numbers with denominator 2^n. We will exploit results on hitting times for the underlying dynamical system on the full shift. In the second part we transfer the results to the beta-shifts. This will give us an estimate on the approximation speed of arbitrary beta-shifts by finite type beta-shifts. This is a particular case of Katok's horseshoe approximation of non-uniformly hyperbolic systems.
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
horseshoes, beta-shifts, Diophantine approximation, non-uniformly hyperbolic systems, SYMBOLIC DYNAMICS, NONCOMPACT SETS
in
Acta Arithmetica
volume
132
issue
3
pages
205 - 230
publisher
Instytut Matematyczny
external identifiers
  • wos:000258703100002
  • scopus:48949093256
ISSN
0065-1036
DOI
10.4064/aa132-3-2
language
English
LU publication?
yes
id
8286bdf8-e5e9-446b-aff2-3e81063e021f (old id 627398)
alternative location
http://www.maths.lth.se/matematiklth/personal/tomasp/pub/2006_3.pdf
date added to LUP
2016-04-01 11:53:00
date last changed
2025-10-14 12:45:59
@article{8286bdf8-e5e9-446b-aff2-3e81063e021f,
  abstract     = {{We consider approximations of real numbers by rational numbers with denominator 2^n. We will exploit results on hitting times for the underlying dynamical system on the full shift. In the second part we transfer the results to the beta-shifts. This will give us an estimate on the approximation speed of arbitrary beta-shifts by finite type beta-shifts. This is a particular case of Katok's horseshoe approximation of non-uniformly hyperbolic systems.}},
  author       = {{Persson, Tomas and Schmeling, Jörg}},
  issn         = {{0065-1036}},
  keywords     = {{horseshoes; beta-shifts; Diophantine approximation; non-uniformly hyperbolic systems; SYMBOLIC DYNAMICS; NONCOMPACT SETS}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{205--230}},
  publisher    = {{Instytut Matematyczny}},
  series       = {{Acta Arithmetica}},
  title        = {{Dyadic Diophantine Approximation and Katok's Horseshoe Approximation}},
  url          = {{http://dx.doi.org/10.4064/aa132-3-2}},
  doi          = {{10.4064/aa132-3-2}},
  volume       = {{132}},
  year         = {{2008}},
}