Dyadic Diophantine Approximation and Katok's Horseshoe Approximation

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Sammanfattning

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.
Originalspråkengelska
Sidor (från-till)205-230
TidskriftActa Arithmetica
Volym132
Nummer3
DOI
StatusPublished - 2008

Ämnesklassifikation (UKÄ)

  • Matematik

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