\(QS129_{1}^{(3)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(129\) | \(42\) | \(1111\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = P_x(x,y) \\ \dot{y} = P_y(x,y) \end{cases}\]
has the following phase portrait done with P4.
The phase portrait appears in the following papers
- With name \(PP20\) in {J. C. Artés, J. Llibre and Huaxin Ou}, Quadratic systems with two invariant straight lines and an invariant hyperbola, {Preprint} (2026).
- With name \(71\) in {B. Coll, A. Ferragut and J. Llibre}, Phase portraits of the quadratic systems with a polynomial inverse integrating factor, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 19} (2009), no.~3, 765--783; MR2533481
- With name \(4.12b\) in {D. Schlomiuk and N. Vulpe}, Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four, emph{Bul. Acad. c{S}tiin c{t}e Repub. Mold. Mat.}, { bf 1 (56)} (2008), 27--83.Note (for name \(4.12b\)): missed arrows
- With name \(PP05\) in {J. Llibre and H. X. Ou}, Quadratic systems with two invariant real straight lines and an invariant parabola, Electron. J. Qual. Theory Differ. Equ. { bf 2025}, Paper No. 66, 54 pp.; MR5018064
- With name \(PP28\) in {J. Llibre and H. X. Ou}, Quadratic systems with two invariant real straight lines and an invariant hyperbola, {Preprint} (2026).
- With name \(P30\) in {J. Llibre and R. D. S. Oliveira}, Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3, Nonlinear Anal. { bf 70} (2009), no. 12, 6378--6379.
- With name \(Ric. 65\) in {J. C. Artés, J. Llibre, D. Schlomiuk and N. Vulpe}, Global analysis of Riccati quadratic differential systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 34} (2024), no.~1, Paper No. 2450004, 46 pp.; MR4701478
- With names \(Fig 31 P1Q\) and \(Fig 34 P1S\) in {A. M. Travaglini}, Integrability and geometryof quadratic differential systems with invariant hyperbolas, {Ph. D., Uni. de Sao Paulo} (2026).
- With name \(Portrait 41\) in {J. C. Artés, J. Llibre and N. Vulpe}, Quadratic systems with an integrable saddle: A complete classification in the coefficient space $ mathbb{R^{12}$}, emph{Nonlinear Anal.}, textbf{75}, no. 14 (2012), 5416--5447.
- With name \(Fig 1.36 f\) in {J. W. Reyn and R. E. Kooij}, Phase portraits of non-degenerate quadratic systems with finite multiplicity two, Differential Equations Dynam. Systems { bf 5} (1997), no.~3-4, 355--414; MR1660222
- With name \(QS129_{1}^{(3)}\) in {J. C. Artés, J. Llibre, D. Schlomiuk and N. Vulpe}, Phase portraits of a family of real quadratic differential systemspossessing a nilpotent or intricate singularity at infinity, {Preprint} (2026).
- With name \(P30\) in {J. C. Artés, J. Llibre and N. Vulpe}, Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space $ Bbb R^{12$}, Rend. Circ. Mat. Palermo (2) { bf 59} (2010), no.~3, 419--449; MR2745521