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Dyadic Diophantine Approximation and Katok's Horseshoe Approximation

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Author

Summary, in English

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.

Department/s

Publishing year

2008

Language

English

Pages

205-230

Publication/Series

Acta Arithmetica

Volume

132

Issue

3

Document type

Journal article

Publisher

Polish Academy of Sciences

Topic

  • Mathematics

Keywords

  • horseshoes
  • beta-shifts
  • Diophantine approximation
  • non-uniformly hyperbolic systems
  • SYMBOLIC DYNAMICS
  • NONCOMPACT SETS

Status

Published

Research group

  • Analysis and Dynamics
  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 0065-1036