Local analytic conjugacy of semi-hyperbolic mappings in two variables, in the non-archimedean setting

Abstract

In this note, we consider locally invertible analytic mappings of a two-dimensional space over a non-archimedean field. Such a map is called semi-hyperbolic if its Jacobian has eigenvalues λ1 and λ2 so that λ1 = 1 and |λ2| ≠ 1. We prove that two analytic semi-hyperbolic maps are analytically equivalent if and only if they are formally equivalent, applying a generalized version of an estimation scheme from our earlier work