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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2009.12771 |
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| _version_ | 1866914838128623616 |
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| author | Chiba, Hayato |
| author_facet | Chiba, Hayato |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_12771 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Normal Forms of $C^\infty$ Vector Fields based on the Renormalization Group Chiba, Hayato Dynamical Systems 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. |
| title | Normal Forms of $C^\infty$ Vector Fields based on the Renormalization Group |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2009.12771 |