Geometric normalization
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911004668985344 |
|---|---|
| author | Chenciner, Alain Sauzin, David Wei, Qiaoling |
| author_facet | Chenciner, Alain Sauzin, David Wei, Qiaoling |
| contents | For a local analytic diffeomorphism of the plane with an irrational elliptic fixed point at 0, we introduce the notion of ``geometric normalization'', which includes the classical formal normalizations as a special case: it is a formal conjugacy to a formal diffeomorphism which preserves the foliation by circles centered at 0. We show that geometric normalizations, despite of non-uniqueness, correspond in a natural way to a unique formal invariant foliation. We show, in various contexts, generic results of divergence for the geometric normalizations, which amount to the generic non-existence of any analytic invariant foliation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric normalization Chenciner, Alain Sauzin, David Wei, Qiaoling Dynamical Systems For a local analytic diffeomorphism of the plane with an irrational elliptic fixed point at 0, we introduce the notion of ``geometric normalization'', which includes the classical formal normalizations as a special case: it is a formal conjugacy to a formal diffeomorphism which preserves the foliation by circles centered at 0. We show that geometric normalizations, despite of non-uniqueness, correspond in a natural way to a unique formal invariant foliation. We show, in various contexts, generic results of divergence for the geometric normalizations, which amount to the generic non-existence of any analytic invariant foliation. |
| title | Geometric normalization |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2506.11580 |