LOCAL ANALYTIC CONJUGACY OF SEMI-HYPERBOLIC MAPPINGS IN TWO VARIABLES, IN THE NON-ARCHIMEDEAN SETTING.

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 [A. Jenkins and S. Spallone, A p-adic approach to local dynamics: Analytic flows and analytic maps tangent to the identity, Ann. Fac. Sci. Toulouse Math. (6) 18(3) (2009) 611-634]. [ABSTRACT FROM AUTHOR]