Abstract
In this paper we consider vector fields in that are invariant under a suitable symmetry and that possess a 'generalized heteroclinic loop' 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 Poincare map, and we prove the existence of infinitely many symmetric periodic orbits near . We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in , and the second one is the charged rhomboidal four-body problem.
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