Periodic orbits for a class of C 1 three-dimensional systems

Antoni Ferragut, Jaume Llibre, Marco Antonio Teixeira

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1 Citation (Scopus)


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 languageEnglish
Pages (from-to)101-115
JournalRendiconti del Circolo Matematico di Palermo
Issue number1
Publication statusPublished - 1 Feb 2007


  • periodic orbit

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