In this paper we consider vector fields in R3 that are invariant under a
suitable symmetry and that posses 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 ...»»»»
In this paper we consider vector fields in R3 that are invariant under a
suitable symmetry and that posses 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 analyze the dynamics of the vector
field near the heteroclinic loop L by means of a convenient Poincar´e 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.^^^^