On the $ C^{8/3} $-Regularisation of Simultaneous Binary Collisions in the Planar 4-Body Problem
| Autor: | Duignan, Nathan, Dullin, Holger R. |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Nonlinearity 34 (2021) 4944-4982 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1361-6544/ac0127 |
| Popis: | The dynamics of the 4-body problem allows for two binary collisions to occur simultaneously. It is known that in the collinear 4-body problem this simultaneous binary collision (SBC) can be block-regularised, but that the resulting block map is only $C^{8/3}$ differentiable. In this paper, it is proved that the $C^{8/3}$ differentiability persists for the SBC in the planar 4-body problem. The proof uses several geometric tools, namely, blow-up, normal forms, dynamics near normally hyperbolic manifolds of equilibrium points, and Dulac maps. Comment: 34 pages, 4 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|