Abstract
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.
Original language | English |
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Pages (from-to) | 101-115 |
Journal | Rendiconti del Circolo Matematico di Palermo |
Volume | 56 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Feb 2007 |
Keywords
- periodic orbit