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

Antoni Ferragut, Jaume Llibre, Marco Antonio Teixeira

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)101-115
JournalRendiconti del Circolo Matematico di Palermo
Volume56
Issue number1
DOIs
Publication statusPublished - 1 Feb 2007

Keywords

  • periodic orbit

Fingerprint Dive into the research topics of 'Periodic orbits for a class of C <sup>1</sup> three-dimensional systems'. Together they form a unique fingerprint.

Cite this