Structurally stable non-degenerate singularities of integrable systems
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915292041445376 |
|---|---|
| author | Kudryavtseva, E. A. Oshemkov, A. A. |
| author_facet | Kudryavtseva, E. A. Oshemkov, A. A. |
| contents | In this paper, we study singularities of the Lagrangian fibration given by a completely integrable system. We prove that a non-degenerate singular fibre satisfying the so-called connectedness condition is structurally stable under (small enough) real-analytic integrable perturbations of the system. In other words, the topology of the fibration in a neighbourhood of such a fibre is preserved after any such perturbation. As an illustration, we show that a saddle-saddle singularity of the Kovalevskaya top is structurally stable under real-analytic integrable perturbations, but structurally unstable under $C^\infty$ smooth integrable perturbations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_00130 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Structurally stable non-degenerate singularities of integrable systems Kudryavtseva, E. A. Oshemkov, A. A. Dynamical Systems Differential Geometry Symplectic Geometry 37J35, 37J39, 53D20, 70E40 In this paper, we study singularities of the Lagrangian fibration given by a completely integrable system. We prove that a non-degenerate singular fibre satisfying the so-called connectedness condition is structurally stable under (small enough) real-analytic integrable perturbations of the system. In other words, the topology of the fibration in a neighbourhood of such a fibre is preserved after any such perturbation. As an illustration, we show that a saddle-saddle singularity of the Kovalevskaya top is structurally stable under real-analytic integrable perturbations, but structurally unstable under $C^\infty$ smooth integrable perturbations. |
| title | Structurally stable non-degenerate singularities of integrable systems |
| topic | Dynamical Systems Differential Geometry Symplectic Geometry 37J35, 37J39, 53D20, 70E40 |
| url | https://arxiv.org/abs/2112.00130 |