\(QS64_{1}^{(3)}\)
Description
Phase Portrait
Topological Invariants
| TCSP |
|---|
| \(64\) |
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 \(C 2S10\) in {J. C. Artés, C. Bujac, D. Schlomiuk and N. Vulpe}, Phase portraits of real quadratic differential systems possessing an invariant ellipse, {Preprint} (2026).
- With name \(14\) in {A. Belfar and R. Benterki}, Qualitative dynamics of quadratic systems exhibiting reducible invariant algebraic curve of degree 3, Palest. J. Math. { bf 11} (2022), Special Issue II, 1--12; MR4447008
- With name \(86\) 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 \(4.45a\) 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 name \(24\) in {A. Ferragut, J. D. García-Saldaña and C. Valls}, Phase portraits of Abel quadratic differential systems of second kind with symmetries, Dyn. Syst. { bf 34} (2019), no.~2, 301--333; MR3941199Note (for name \(24\)): Elliptic orbit missed. Position does not matter.
- With name \(L5\) in {J. Llibre and J. Yu}, Global phase portraits of quadratic systems with an ellipse and a straight line as invariant algebraic curves, Electron. J. Differential Equations { bf 2015}, No. 314, 14 pp.; MR3441696
- With name \(P21\) 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 \(Fig. 07\) in {J. Llibre and C. Pantazi}, Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023), no. 1, Paper No. 2350003, 54 pp.
- With name \(21\) 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; MR1792982Note (for name \(21\)): uncompleted seps
- With name \(S IV 20\) in {J. C. Artés, J. Llibre, D. Schlomiuk and N. Vulpe}, Abel quadratic differential systems of second kind, Electron. J. Differential Equations { bf 2024}, Paper No. 50, 38 pp.; MR4793966
- With name \(Portrait 35\) 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 names \(Fig6 3\), \(Fig6 4\) and \(Fig8 6\) in {P. de Jager}, Phase portraits for quadratic systems with a higher order singularity with two zero eigenvalues, emph{J. Differential Equations}, textbf{87} (1990), 169--204.
- With name \(P21\) 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