On the dihedral n-body problem

Details On the dihedral n-body problem On the dihedral n-body problem

2007-07-24

arxiv.org/abs/0707.3598v2

Mathematics

Dynamical Systems

Second version. In the first there was a mistake in a proof: some section had been omitted

Scientific paper

10.1088/0951-7715/21/6/009

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 D_l, where D_l 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.

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