Electron. J. Differential Equations,
Vol. 2019 (2019), No. 15, pp. 1-25.
Phase portraits of quadratic polynomial differential systems having
as solution some classical planar algebraic curves of degree 4
Rebiha Benterki, Jaume Llibre
Abstract:
We classify the phase portraits of quadratic polynomial differential
systems having some relevant classic quartic algebraic curves as
invariant algebraic curves, i.e. these curves are formed by orbits of
the quadratic polynomial differential system.
More precisely, we realize 16 different well-known algebraic curves
of degree 4 as invariant curves inside the quadratic polynomial
differential systems. These realizations produce 31 topologically
different phase portraits in the Poincare disc for such quadratic
polynomial differential systems.
Submitted June 15, 2018. Published January 28, 2019.
Math Subject Classifications: 34C15, 34C25.
Key Words: Quadratic differential system; Poincare disc;
invariant algebraic curve.
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Rebiha Benterki
Département de Mathématiques
Université Bachir El Ibrahimi
Bordj Bou Arréridj 34265
El Anasser, Algeria
email: r.benterki@univ-bba.dz
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Jaume Llibre
Departament de Matematiques
Universitat Autònoma de Barcelona
08193 Bellaterra
Barcelona, Catalonia, Spain
email: jllibre@mat.uab.cat
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