18 citations · 80 across the 17 of their papers we have counts for
4 papers · 2 filters
Chazy-Type Asymptotics and Hyperbolic Scattering for the -Body Problem
Nathan Duignan, Richard Moeckel, Richard Montgomery +1
We study solutions of the Newtonian -body problem which tend to infinity hyperbolically, that is, all mutual distances tend to infinity with nonzero speed as $t \rightarrow +\in…
On the -Regularisation of Simultaneous Binary Collisions in the Collinear 4-Body Problem
Nathan Duignan, Holger R. Dullin
The singularity at a simultaneous binary collision is explored in the collinear 4-body problem. It is known that any attempt to remove the singularity via block regularisation will…
Normal Forms for Manifolds of Normally Hyperbolic Singularities and Asymptotic Properties of Nearby Transitions
Nathan Duignan
This paper contains theory on two related topics relevant to manifolds of normally hyperbolic singularities. First, theorems on the formal and normal forms for these object…
Regularisation for Planar Vector Fields
Nathan Duignan, Holger Dullin
This paper serves as a first foray on regularisation for planar vector fields. Motivated by singularities in celestial mechanics, the block regularisation of a generic class of deg…