Dyadic Diophantine Approximation and Katok's Horseshoe Approximation

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.

• Författare: Tomas Persson; Jörg Schmeling
• Avdelning/ar: Matematik LTH; Dynamical systems
• Publiceringsår: 2008
• Språk: Engelska
• Sidor: 205-230
• Publikation/Tidskrift/Serie: Acta Arithmetica
• Volym: 132
• Issue: 3
• Länkar: http://www.maths.lth.se/matematiklth/personal/tomasp/pub/2006_3.pdf; http://dx.doi.org/10.4064/aa132-3-2
• Dokumenttyp: Artikel i tidskrift
• Förlag: Polish Academy of Sciences
• Ämne: Mathematics
• Nyckelord: horseshoes; beta-shifts; Diophantine approximation; non-uniformly hyperbolic systems; SYMBOLIC DYNAMICS; NONCOMPACT SETS
• Status: Published
• Forskningsgrupp: Analysis and Dynamics; Dynamical systems
• ISBN/ISSN/Övrigt: ISSN: 0065-1036