On hyperbolic fixed points in ultrametric dynamics

Abstract

Let K be a complete ultrametric field. We give lower and upper bounds for the size of linearization discs for power series over K near hyperbolic fixed points. These estimates are maximal in the sense that there exist examples where these estimates give the exact size of the corresponding linearization disc. In particular, at repelling fixed points, the linearization disc is equal to the maximal disc on which the power series is injective.Comment: http://www.springerlink.com/content/?k=doi%3a%2810.1134%2fS2070046610030052%2

The size of quadratic p -adic linearization disks

“…For results in fields of caracteristic zero-equal characteristic case, see [18]. In the hyperbolic case |λ| = 1, 0, the linearization disk will in general be the maximal disk of injectivity [20]. (…”

Residue fixed point index and wildly ramified power series

“…Such power series are called wildly ramified. † See, for example, [9,12,23,25] for background on wildly ramified power series, [8, 11, 14-16, 19, 21] for results related to this paper, and [6,13,17,22] and references therein for local dynamics of analytic germs in positive characteristic. See also, for example, [4,7] and references therein, for the myriad of group-theoretic results about the 'Nottingham group', which is the group under composition formed by the wildly ramified power series.…”