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

Antoni Ferragut; Jaume Llibre; Marco Antonio Teixeira

doi:10.1007/BF03031432

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

Antoni Ferragut, Jaume Llibre, Marco Antonio Teixeira

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-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 language	English
Pages (from-to)	101-115
Journal	Rendiconti del Circolo Matematico di Palermo
Volume	56
Issue number	1
DOIs	https://doi.org/10.1007/BF03031432
Publication status	Published - 1 Feb 2007

Keywords

periodic orbit

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title = "Periodic orbits for a class of C 1 three-dimensional systems",

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. {\textcopyright} 2007 Springer.",

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AB - 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.

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