Quadratic vector fields in the plane have a finite number of limit cycles
Publications Mathématiques de l'IHÉS, Tome 64 (1986), pp. 111-142.
@article{PMIHES_1986__64__111_0,
     author = {Bamon, Rodrigo},
     title = {Quadratic vector fields in the plane have a finite number of limit cycles},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {111--142},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {64},
     year = {1986},
     mrnumber = {88d:58095},
     zbl = {0625.58028},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1986__64__111_0/}
}
TY  - JOUR
AU  - Bamon, Rodrigo
TI  - Quadratic vector fields in the plane have a finite number of limit cycles
JO  - Publications Mathématiques de l'IHÉS
PY  - 1986
SP  - 111
EP  - 142
VL  - 64
PB  - Institut des Hautes Études Scientifiques
UR  - http://archive.numdam.org/item/PMIHES_1986__64__111_0/
LA  - en
ID  - PMIHES_1986__64__111_0
ER  - 
%0 Journal Article
%A Bamon, Rodrigo
%T Quadratic vector fields in the plane have a finite number of limit cycles
%J Publications Mathématiques de l'IHÉS
%D 1986
%P 111-142
%V 64
%I Institut des Hautes Études Scientifiques
%U http://archive.numdam.org/item/PMIHES_1986__64__111_0/
%G en
%F PMIHES_1986__64__111_0
Bamon, Rodrigo. Quadratic vector fields in the plane have a finite number of limit cycles. Publications Mathématiques de l'IHÉS, Tome 64 (1986), pp. 111-142. http://archive.numdam.org/item/PMIHES_1986__64__111_0/

[A] A. Andronov et al., Qualitative Theory of Second Order Dynamical Systems, John Wiley & Sons, New York, 1973. | MR | Zbl

[C] W. Coppel, A survey of Quadratic Systems, Journal of Differential Equations, 2 (1966), 293-304. | MR | Zbl

[Ca] J. Carr, Applications of Center Manifold Theory, Applied Math. Sciences, 35, Springer-Verlag, 1981. | MR | Zbl

[Ch-S] C. Chicone and S. Schafer, Separatrix and Limit Cycles of Quadratic Systems and Dulac's Theorem, Transactions Amer. Math. Soc., 278 (1983), 585-612. | MR | Zbl

[D] M. H. Dulac, Sur les cycles limites, Bull. Soc. Math. France, 51 (1923), 45-188. | JFM | Numdam

[Du] F. Dumortier, Singularities of Vector Fields, Journal of Differential Equations, 23, I (1977), 53-106. | MR | Zbl

[H-P-S] M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds, Springer Lecture Notes in Math., 583 (1977). | MR | Zbl

[I] Yu. S. Il'Yašenko, Limit cycles of polynomial vector fields with non degenerate singular points in the real plane (in Russian), Functional Analysis and its applications, 18 (3) (1984), 32-34 (in translation : 18 (3) (1985), 199-209). | Zbl

[P-L1] I. G. Petrovskii and E. U. Landis, On the number of limit cycles of the equation dy/dx = P(x,y)/Q(x,y) where P and Q are polynomials of the second degree, Amer. Math. Soc. Transl. (2), 16 (1958), 177-221. | MR | Zbl

[P-L2] I. G. Petrovskii and E. U. Landis, On the number of limit cycles of the equation dy/dx = P(x,y)/Q(x,y) where P and Q are polynomials, Amer. Math. Soc. Transl. (2), 14 (1960), 181-200. | MR | Zbl

[P-L3] I. G. Petrovskii and E. U. Landis, Corrections to the articles : "On the number of limit cycles of the equation dy/dx = P(x,y)/Q(x,y) where P and Q are polynomials", Math. Sb.N.S., 48 (90) (1959). 253-255. | MR

[P-M] J. Palis and W. De Melo, Geometric Theory of Dynamical Systems ; An Introduction, New York, Springer-Verlag, 1982. | MR | Zbl

[S] J. Sotomayor, Curvas definidas por equaçoes diferenciais no plano, 13° Colóquio Bras. de Mat., IMPA, 1981. | MR

[Sh1] Shi Songling, A concrete example of the existence of four limit cycles for plane quadratic systems, Sci., Sinica, Ser. A, 23 (1980), 153-158. | MR | Zbl

[Sh2] Shi Songling, A method for constructing cycles without contact around a weak focus, Journal of Differential Equations, 41 (1981), 301-312. | MR | Zbl