Results of theoretical and numerical investigations concerning the space-time evolution in
nd of Coulombian
systems known in Plasma Physics and Newtonian systems known in Cosmology are reported here. A generic, canonical Hamiltonian formulation is given (1) for studying
single speed solutions of their Coulomb- or Jeans–Vlasov–Poisson descriptions. (2) It is shown that their
equations of motion are integrable for vorticity free planar motions in
nD (3) and that their characteristics are solutions of explicit non-linear ODEs in general (4). Some simple examples of trajectories are illustrated and the problem of their crossing is evoked.
More abstracts about the Single speed solutions of the Vlasov–Poisson equations for Coulombian and Newtonian systems in nD