Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2009.12771 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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.