Dynamics for<i>β</i>-shifts and Diophantine approximation
Dynamics for<i>β</i>-shifts and Diophantine approximation
Abstract We investigate the β -expansion of an algebraic number in an algebraic base β . Using tools from Diophantine approximation, we prove several results that may suggest a strong difference between the asymptotic behaviour of eventually periodic expansions and that of non-eventually periodic expansions.