2007/07/31 by Davide L. Ferrario, Alessandro Portaluri · 1 citation
Mathematics · #math.DS #msc:70F10 #msc:37C80
paper · pdf · doi:10.1088/0951-7715/21/6/009
Second version. In the first there was a mistake in a proof: some section had been omitted
arxiv created 2008/03/11 · arxiv updated 2009/12/01
Consider n=2l>=4 point particles with equal masses in space, subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group Dl, where Dl is the group of order 2l generated by two rotations of angle pi around two secant lines in space meeting at an angle of pi/l. By adding a homogeneous gravitational (Newtonian) potential one finds a special n-body problem with three degrees of freedom, which is a kind of generalisation of Devaney isosceles problem, in which all orbits have zero angular momentum. In the paper we find all the central configurations and we compute the dimension of the stable/unstable manifolds.