TY - JOUR
T1 - Quadratic systems with an invariant algebraic curve of degree 3 and a darboux invariant
AU - Llibre, Jaume
AU - Oliveira, Regilene D.S.
AU - Rodrigues, Camila A.B.
N1 - Publisher Copyright:
© 2021. Texas State University - San Marcos. All rghts reserved.
PY - 2021
Y1 - 2021
N2 - Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(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 f(x, y)est, with s ∈ R.
AB - Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(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 f(x, y)est, with s ∈ R.
KW - Algebraic invariant curve
KW - Darboux invariant
KW - Global phase portrait
KW - Quadratic vector fields
UR - http://www.scopus.com/inward/record.url?scp=85115796562&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85115796562
SN - 1072-6691
VL - 2021
JO - Electronic Journal of Differential Equations
JF - Electronic Journal of Differential Equations
ER -