Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant

dc.contributor.authorLlibre, Jaume
dc.contributor.authorOliveira, Regilene
dc.contributor.authorRodrigues, Camila A. B.
dc.date.accessioned2021-08-27T18:57:35Z
dc.date.available2021-08-27T18:57:35Z
dc.date.issued2021-08-16
dc.description.abstractLet QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic ƒ(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normal forms for the quadratic systems in QS3. Working with these normal forms we complete the characterization of the phase portraits in QS3 having a Darboux invariant of the form ƒ(x, y) est, with s ∈ ℝ.
dc.description.departmentMathematics
dc.formatText
dc.format.extent52 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationLlibre, J., Oliveira, R. D. S., Rodrigues, C. A. B. (2021). Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant. <i>Electronic Journal of Differential Equations, 2021</i>(69), pp. 1-52.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14479
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectQuadratic vector fields
dc.subjectAlgebraic invariant curve
dc.subjectDarboux invariant
dc.subjectGlobal phase portrait
dc.titleQuadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant
dc.typeArticle

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