论文标题
$ c^\ infty $ vector字段的正常形式基于重新归一化组
Normal Forms of $C^\infty$ Vector Fields based on the Renormalization Group
论文作者
论文摘要
多项式矢量场的正常形式理论扩展到$ c^\ infty $ vector Fields在起源中消失的范围。 $ C^\ infty $正常形式的显式公式和将矢量场带入其正常形式的近乎身份转换是通过重新规范化组方法获得的。通过其正常形式研究了给定矢量场的动力学，例如不变歧管的存在。 $ c^\ infty $正常形式理论用于证明存在两个维度系统的许多周期性轨道的存在，这些轨道并未从多项式正常形式中显示。
The normal form theory for polynomial vector fields is extended to those for $C^\infty$ vector fields vanishing at the origin. Explicit formulas for the $C^\infty$ normal form and the near identity transformation which brings a vector field into its normal form are obtained by means of the renormalization group method. The dynamics of a given vector field such as the existence of invariant manifolds is investigated via its normal form. The $C^\infty$ normal form theory is applied to prove the existence of infinitely many periodic orbits of two dimensional systems which is not shown from polynomial normal forms.
