二元共振解析映射的局部解析共轭性
Local analytic conjugacy of resonant analytic mappings in two variables, in the non-archimedean setting
摘要：
本文考虑二维局部可逆解析映射，其系数在非阿基米德域上。假设这样的映射有一个雅可比矩阵，其特征值为$λ_1$和$λ_2$，使得$|λ_1|>1$和$λ_2$是$λ_1$的正幂，或者$λ_1=1$和$|λ_2|\neq 1$。我们证明了两个形式映射的特征值满足这些条件之一是解析等价的当且仅当它们是形式等价的。
英文摘要：
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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