Perturbation theory and canonical coordinates in celestial mechanics
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929317760466944 |
|---|---|
| author | Pinzari, Gabriella |
| author_facet | Pinzari, Gabriella |
| contents | KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by V.I.Arnold in the 60s who worked out a theorem, that he named the Fundamental Theorem (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively taking the invariance by rotation and close-to-integrability into account was used. Since then, some progress has been done in the symplectic assessment of the problem, and here we review such results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_07457 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Perturbation theory and canonical coordinates in celestial mechanics Pinzari, Gabriella Dynamical Systems Mathematical Physics numbers: primary: 34C20, 70F10, 37J10, 37J15, 37J40, secondary: 34D10, 70F07, 70F15, 37J25, 37J35 KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by V.I.Arnold in the 60s who worked out a theorem, that he named the Fundamental Theorem (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively taking the invariance by rotation and close-to-integrability into account was used. Since then, some progress has been done in the symplectic assessment of the problem, and here we review such results. |
| title | Perturbation theory and canonical coordinates in celestial mechanics |
| topic | Dynamical Systems Mathematical Physics numbers: primary: 34C20, 70F10, 37J10, 37J15, 37J40, secondary: 34D10, 70F07, 70F15, 37J25, 37J35 |
| url | https://arxiv.org/abs/2209.07457 |