SEMINARIO DI FISICA MATEMATICA
15:00-16:00, Sala Riunioni (Dip. Matematica)
Some special periodic solutions of the Newtonian N-body problem
Giorgio Fusco (Universita' di L’Aquila)
http://adams.dm.unipi.it/~fismat/FisMat.html

We consider the motion of N \in {12, 24, 60} equal particles subjected
to Newton gravitational interaction. The numbers 12, 24, 60 are the
orders of the rotation groups of the Platonic Polyhedra. By imposing
both symmetry and topological constraints we define certain cones K
\in W^{1,2}(T,R^{3N}), (W^{1,2}(T,R^{3N}) the set of T−periodic maps
u : R \to R^{3N}), associated to Platonic Polyhedra and such that the
hamiltonian action A is coercive on K. We show that the corresponding
minimizers are collision-free and therefore genuine periodic motions
of the N−body problem with a rich symmetric structure.