Symmetric periodic orbits near a heteroclinic loop
نویسندگان
چکیده
In this paper we consider vector fields in R 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 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 R, and the second one is the charged rhomboidal four body problem.
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