\(QS078_2\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(78\) | \(440\) | \(3201\) |
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 \(23\) in {B. García, J. Llibre and J. S. Pérez del Río}, Phase portraits of the quadratic vector fields with a polynomial first integral, Rend. Circ. Mat. Palermo (2) { bf 55} (2006), no.~3, 420--440; MR2287071
- With name \(A 3.7L1\) in {J. C. Artés, M. C. Mota and A. C. Rezende}, Quadratic systems possessing an infinite elliptic-saddle or an infinite nilpotent saddle, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 34} (2024), no.~11, Paper No. 2430023, 43 pp.; MR4801966
- With name \(5.8L2\) in {J. C. Artés and L. Cairó}, Phase portraits of quadratic differential systems with a weak focus and a (1,1) SN, {Preprint} (2026).
- With name \(vulpe6\) in {J. C. Artés and J. Llibre}, Quadratic Hamiltonian vector fields, emph{J. Differential Equations}, { bf 107} (1994), 80--95.
- With name \(Vul 6\) 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 \(Fig11.5c (9)\) in {J. W. Reyn and X. H. Huang}, Phase portraits of quadratic systems with finite multiplicity three and a degenerate critical point at infinity, Rocky Mountain J. Math. { bf 27} (1997), no.~3, 929--978; MR1490285
- With name \(QS078_2\) 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 \(Vul6\) in {N. I. Vulpe}, Affine--invariant conditions for the topological distinction of quadratic systems with a center (in Russian), emph{Differentsial'nye Uravneniya}, textbf{19}, no. 3 (1983), 371--379. (Translation in emph{Differential Equations}, textbf{19} (1983), {273--280}.)