For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an
open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial
vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools
for proving this result are, first, ...»»»»
For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an
open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial
vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools
for proving this result are, first, the existence in the phase portrait of a symmetry with respect
to a plane and, second, the existence of two symmetric heteroclinic loops.^^^^