Quantitative KAM theory, with an application to the three-body problem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909247681331200 |
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| author | Pinzari, Gabriella Liu, Xiang |
| author_facet | Pinzari, Gabriella Liu, Xiang |
| contents | Based on quantitative ``{\sc kam} theory'', we state and prove two theorems about the continuation of maximal and whiskered quasi--periodic motions to slightly perturbed systems exhibiting proper degeneracy. Next, we apply such results to prove that, in the three--body problem, there is a small set in phase space where it is possible to detect both such families of tori. We also estimate the density of such motions in proper ambient spaces.
Up to our knowledge, this is the first proof of co--existence of stable and whiskered tori in a physical system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00279 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantitative KAM theory, with an application to the three-body problem Pinzari, Gabriella Liu, Xiang Dynamical Systems Mathematical Physics 2020: 37J40, 37J11, 37J06 Based on quantitative ``{\sc kam} theory'', we state and prove two theorems about the continuation of maximal and whiskered quasi--periodic motions to slightly perturbed systems exhibiting proper degeneracy. Next, we apply such results to prove that, in the three--body problem, there is a small set in phase space where it is possible to detect both such families of tori. We also estimate the density of such motions in proper ambient spaces. Up to our knowledge, this is the first proof of co--existence of stable and whiskered tori in a physical system. |
| title | Quantitative KAM theory, with an application to the three-body problem |
| topic | Dynamical Systems Mathematical Physics 2020: 37J40, 37J11, 37J06 |
| url | https://arxiv.org/abs/2302.00279 |