ON CRITICAL EXPO NENTS I N FIXED PO INTS OF k -UNIFO RM BI NARY MORPHISMS

Let w be an infinite fixed point of a binary k -uniformmorphism f ,andletE ( w ) be the critical exponent of w .Wegivenecessary and sufficient conditions for E ( w ) to be bounded, and anexplicit formula to compute it when it is. In particular, we show thatE ( w ) is always rational. We also sketch an extension of our method tonon-uniform morphisms over general alphabets