3 papers
math.DS2019
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…
math.DS2019
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…
math.DS2019
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…