In this paper we will find a continuous of periodic orbits passing
near infinity for a class of polynomial vector fields in R3. We consider
polynomial vector fields that are invariant under a symmetry with
respect to a plane and that possess a “generalized heteroclinic loop”
formed by two singular points e+ and e− at infinity ...»»»»
In this paper we will find a continuous of periodic orbits passing
near infinity for a class of polynomial vector fields in R3. We consider
polynomial vector fields that are invariant under a symmetry with
respect to a plane and that possess a “generalized heteroclinic loop”
formed by two singular points e+ and e− at infinity and their invariant
manifolds � and . � is an invariant manifold of dimension 1 formed
by an orbit going from e− to e+, � is contained in R3 and is transversal
to . is an invariant manifold of dimension 2 at infinity. In fact, is
the 2–dimensional sphere at infinity in the Poincar´e compactification
minus the singular points e+ and e−. The main tool for proving the
existence of such periodic orbits is the construction of a Poincar´e map
along the generalized heteroclinic loop together with the symmetry
with respect to .^^^^
CORBERA SUBIRANA, Montserrat; LLIBRE, Jaume. "Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimensions 1 and 2 in R-3". A: International Journal of Bifurcation and Chaos, 2007, vol. 17, núm. 9, pàg. 3295-3302.