On the C8/3-regularisation of simultaneous binary collisions in the planar four-body problem. (25th June 2021)

• Record Type: Journal Article
• Authors: Duignan, Nathan; Dullin, Holger R
• Is Part Of: Nonlinearity. Volume 34:Number 7(2021)
• Page Start: 4944
• Page End: 4982
• Publication Date: 2021-06-25
• Subjects: normally hyperbolic -- blow-up -- collisions -- regularisation -- celestial mechanics -- normal forms; 70F16 -- 70F10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac0127
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: The dynamics of the four-body problem allows for two binary collisions to occur simultaneously. It is known that in the collinear four-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 four-body problem. The proof uses several geometric tools, namely, blow-up, normal forms, dynamics near normally hyperbolic manifolds of equilibrium points, and Dulac maps.