Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant
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Date
2021-08-16
Authors
Llibre, Jaume
Oliveira, Regilene
Rodrigues, Camila A. B.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
Let 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.
Description
Keywords
Quadratic vector fields, Algebraic invariant curve, Darboux invariant, Global phase portrait
Citation
Llibre, 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.
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Attribution 4.0 International