A Sharper Estimation of Analytic Conjugacies in the Non-archimedean Setting

We look at the conjugacy of mappings of the form f(x) = x + ∑ anx . The goal of this paper is to further develop an approach of Jenkins and Spallone [7] which is both elementary and effective in constructing convergent power series conjugating two such functions (recall that two such maps f and g are conjugate if there is an h so that h ◦ f ◦ h−1 = g). Using this approach, we are also able to construct groups of germs. We take the time to explain all concepts, and knowledge of power series is the only prerequisite required for reading. This work arose out of research performed during the Kansas State University Research Experience for Undergraduates.