  We show that if the complexity difference function p(n+1)-p(n) of a infinite
minimal shift is bounded, then the the automorphism group of the one-sided
shift is finite, and the automorphism group of the corresponding two-sided
shift "modulo the shift" is finite. For the minimal Sturmian and minimal
substitution shifts, the bounds can be explicitly computed, and for linearly
recurrent shifts, the bound can be expressed as a function of the linear
recurrence constant. We also show that any endomorphism of a linearly recurrent
shift is a root of a power of the shift map.
