Dyadic Diophantine Approximation and Katok's Horseshoe Approximation
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