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Dyadic Diophantine Approximation and Katok's Horseshoe Approximation

Persson, Tomas LU 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.
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author
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
Polish Academy of Sciences
external identifiers
  • wos:000258703100002
ISSN
0065-1036
language
English
LU publication?
yes
id
8286bdf8-e5e9-446b-aff2-3e81063e021f (old id 627398)
date added to LUP
2008-09-15 11:07:08
date last changed
2017-03-16 14:24:01
@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},
  keyword      = {horseshoes,beta-shifts,Diophantine approximation,non-uniformly hyperbolic systems,SYMBOLIC DYNAMICS,NONCOMPACT SETS},
  language     = {eng},
  number       = {3},
  pages        = {205--230},
  publisher    = {Polish Academy of Sciences},
  series       = {Acta Arithmetica},
  title        = {Dyadic Diophantine Approximation and Katok's Horseshoe Approximation},
  volume       = {132},
  year         = {2008},
}