18 citations · 80 across the 17 of their papers we have counts for
4 papers · 1 filter
Blow-Up, Asymptotics, and Improbability of Collision Singularities in the n-Body Problem
Nathan Duignan, Manuel Quaschner
We study finite-time singularities in -body systems with pair potentials that are homogeneous of degree , where , that are not necessarily attractive and with bounded…
Global realisation of magnetic fields as 1D Hamiltonian systems
Nathan Duignan, David Perrella, David Pfefferlé
The paper reviews the notion of D non-autonomous Hamiltonian systems, portraying their dynamics as the flow of the Reeb field related to a closed two-form of maximal…
Normal Forms and Near-Axis Expansions for Beltrami Magnetic Fields
Nathan Duignan, James D. Meiss
A formal series transformation to Birkhoff-Gustavson normal form is obtained for toroidal magnetic field configurations in the neighborhood of a magnetic axis. Bishop's rotation-mi…
Integrability, Normal Forms, and Magnetic Axis Coordinates
Joshua W. Burby, Nathan Duignan, James D. Meiss
Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation cons…