论文标题
平面谐振鞍向量场的分析法线形式
Analytic normal forms for planar resonant saddle vector fields
论文作者
论文摘要
我们为在孤立的奇异性附近的复杂平面的全体形态矢量场的细菌（即P：q resonant-saddle）提供了基本独特的``正常形式''。因此，该类型的每个矢量场都是共轭的，是通过奇异性的生物形态图的胚芽到显式矢量场家族的首选元素上的。这些模型矢量场在谐振单元中是多项式。这项工作是对与身份相切的抛物线差构象获得的类似结果的后续后续，并解决了为共鸣鞍向量场找到明确的局部分析模型的长期存在问题。
We give essentially unique ``normal forms'' for germs of a holomorphic vector field of the complex plane in the neighborhood of an isolated singularity which is a p:q resonant-saddle. Hence each vector field of that type is conjugate, by a germ of a biholomorphic map at the singularity, to a preferred element of an explicit family of vector fields. These model vector fields are polynomial in the resonant monomial.Abstract. This work is a followup of a similar result obtained for parabolic diffeomorphisms which are tangent to the identity, and solves the long standing problem of finding explicit local analytic models for resonant saddle vector fields.
