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Dyadic Diophantine Approximation and Katok's Horseshoe Approximation

By Tomas Persson and Jörg Schmeling

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

Topics: Mathematics, horseshoes, beta-shifts, Diophantine approximation, non-uniformly hyperbolic systems, SYMBOLIC DYNAMICS, NONCOMPACT SETS
Publisher: 'Institute of Mathematics, Polish Academy of Sciences'
Year: 2008
DOI identifier: 10.4064/aa132-3-2
OAI identifier: oai:lup.lub.lu.se:8286bdf8-e5e9-446b-aff2-3e81063e021f
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