Characteristic words as fixed points of homomorphisms

Abstract

With each real number 0, 0 < 0 < 1, we can associate the so-called characteristic word w = w(0), defined by wn = [(n+1)0]-[n0], for n>1. We prove the following: if 0 has a purely periodic continued fraction expansion, then w(0) is a fixed point of a certain homomorphism y=y0.