(Both the published version and the arXiv version are available online.)

Let K be a field which is complete with respect to a non-archimedean valuation. Let f(x) be a power series over K whose lowest-degree term is cx, where we assume that c does not have absolute value 1 (or 0). It is easy to see that there is a unique power series L(x) over K whose lowest-degree term is x and for which  L o f(x) = cL(x)  as formal power series. Herman and Yoccoz showed that this identity is valid not just formally, but also when we substitute for x any element of a certain positive-radius disk around the origin. In this paper we determine the largest disk on which this formal conjugacy holds. Our proofs are entirely within the realm of non-archimedean analysis, in contrast to the work of Herman and Yoccoz which essentially showed that the proof of the analogous result over the complex numbers can be extended to more general valued fields.

Michael Zieve:  home page   publication list