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

In this note, we consider locally invertible analytic mappings in two dimensions, with coefficients in a non-archimedean field. Suppose such a map has a Jacobian with eigenvalues $λ_1$ and $λ_2$ so that $|λ_1|>1$ and $λ_2$ is a positive power of $λ_1$, or that $λ_1=1$ and $|λ_2|\neq 1$. We prove that two formal maps with eigenvalues satisfying either of these conditions are analytically equivalent if and only if they are formally equivalent.

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