The main goal of this paper is the analytic classification of the germs of singular foliations generated, up to an analytic change of coordinates, by the germs of vector fields of form the \(x\partial _{x}+{\sum }_{i=1}^{n}a_{i}(x,\mathbf {z})\partial _{z_{i}}\), where a_i(x,z) is a germ of analytic function with a_i(x,0) = 0. We prove, under some hypothesis, that these germs of singular foliations are analytically classified once their local holonomy along a given separatrix is analytically conjugated.

中文翻译：

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解析叶的整体性和等价性

本文的主要目标是通过\（x \ partial _ {x} + {\ sum} _ {I = 1} ^ {N} A_ {I}（X，\ mathbf {Z}）\局部_ {Z_ {I}} \） ，其中，一个_我（X，ž）是解析函数的胚芽一个_i（x，0）=0。我们证明，在某些假设下，一旦奇异叶的这些细菌沿着给定分离线的局部完整性被分析共轭，就可以进行分析分类。