On the numerology of ramification data for power series in characteristic $p$

Abstract: Let $k$ be a perfect field of characteristic $p$ and set $K=k((t))$. In this paper we study the ramification properties of elements of Aut$_k(K)$. By choosing a uniformizer for $K$ we may interpret our theorems in terms of power series over $k$. The most important tool that we use is the field of norms construction of Fontaine and Wintenberger.