Ramification of some automorphisms of local fields

Let k be a perfect field of characteristic p and let gamma is an element of Aut(k((t))). Define the ramification numbers of gamma by i(m) = upsilon(t)(gamma(pm)(t) - t) -1. We give a characterization of the sequences (i(m)) which are the sequences of ramification numbers of infinite order automorphisms of formal power series fields over finite fields. Then, given a perfect field k, we give sufficient conditions on (i(m)) to be the sequence of ramification numbers of an automorphism gamma is an element of Aut(k)(k((t))) and we investigate these sequences (i(m)) in the case where there exists sigma is an element of Aut(k)(k((t))) such that sigma gamma = gamma sigma with sigma not equal gamma(nu) for all gamma is an element of Z(p). (C) Academic Press.