We study C 1 perturbations of a reversible polynomial differential system of degree 4 in ℝ 3. We introduce the concept of strongly reversible vector field. If the perturbation is strongly reversible, the dynamics of the perturbed system does not change. For non-strongly reversible perturbations we prove the existence of an arbitrary number of symmetric periodic orbits. Additionally, we provide a polynomial vector field of degree 4 in ℝ 3 with infinitely many limit cycles in a bounded domain if a generic assumption is satisfied. © 2007 Springer.
|Journal||Rendiconti del Circolo Matematico di Palermo|
|Publication status||Published - 1 Feb 2007|
- periodic orbit