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. © World Scientific Publishing Company.
|Journal||International Journal of Bifurcation and Chaos|
|Publication status||Published - 1 Jan 2006|
- Heteroclinic loop
- Polynomial vector fields
- Symmetric periodic orbits