In this paper we consider vector fields in ℝ3 that are invariant under a suitable symmetry and that possess a 'generalized heteroclinic loop' L formed by two singular points (e+ and e-) and their invariant manifolds: one of dimension 2 (a sphere minus the points e + and e-) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e-). In particular, we analyse the dynamics of the vector field near the heteroclinic loop by means of a convenient Poincaré map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in ℝ3, and the second one is the charged rhomboidal four-body problem. © 2006 IOP Publishing Ltd.
|Journal||Journal of Physics A: Mathematical and General|
|Publication status||Published - 15 Dec 2006|