A preparation theorem for codimension-one foliations

• 成果类型: Article
• 署名作者: Loray, Frank
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.163.709
• 发表日期: 2006
• 页码: 709-722
• 关键词: formal normal-form; analytical classification

摘要

After gluing foliated complex manifolds, we derive a preparation-like theorem for singularities of codimension-one foliations and planar vector fields (in the real or complex setting). Without computation, we retrieve and improve results of Levinson-Moser for functions, Dufour-Zhitomirskii for nondegenerate codimension-one foliations (proving in turn the analyticity), Strozyna-Zoladek for non degenerate planar vector fields and Bruno-Ecalle for saddle-node foliations in the plane.