\(QS138_{1}^{(3)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Inf Sep |
|---|---|
| \(138\) | \(1111\) |
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 \(Fig 7 24\) in {L. Cairó and J. Llibre}, Phase portraits of Families VII and VIII of the Quadratic Systems. Axioms. No. 12(756), (2023), 18pp.
- With name \(50\) 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 \(4.43a\) 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.
- With names \(5.25\) and \(5.29\) in {D. Schlomiuk and N. Vulpe}, Integrals and phase portraits of planar quadratic differential systems with invariant lines of at least five total multiplicity, emph{Rocky Mountain J. Math.}, textbf{38}, no. 6 (2008), 2015--2075.
- With name \(Fig 1 B1-1S4\) in {J. C. Artés, L. Cairó and J. Llibre}, New Exploration of Phase portraits Classification of QuadraticPolynomial Differential Systems based on Invariant Theory. Applied Math. No. 1(0), (2025), 24pp.
- With name \(PP24\) in {J. Llibre and H. X. Ou}, Quadratic systems with two invariant real straight lines and an invariant hyperbola, {Preprint} (2026).
- With name \(P31\) 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 \(32\) in {M. Ndiaye and H. J. Giacomini}, Quadratic systems equivalent by domains to a linear one: global phase portraits, Extracta Math. { bf 15} (2000), no.~1, 97--119; MR1792982
- With names \(Fig1 E^-1M^2_4,2\) and \(Fig2 M^-1_02,1M^2_2,2(a)\) in {J. W. Reyn}, Phase portraits of quadratic systems without finite critical points, Nonlinear Anal. { bf 27} (1996), no.~2, 207--222; MR1389478
- With name \(Ric. 63\) 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 \(Fig 31 P4Q\) and \(Fig 35 P1T\) in {A. M. Travaglini}, Integrability and geometryof quadratic differential systems with invariant hyperbolas, {Ph. D., Uni. de Sao Paulo} (2026).
- With name \(17\) in {A. Gasull, S. Li Ren and J. Llibre}, Chordal quadratic systems, emph{Rocky Mountain J. Math.}, textbf{16}, no. 4 (1986), 751--782.
- With name \(Fig 1.34 b\) 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 \(QS138_{1}^{(3)}\) 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 \(P31\) 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