@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] Qualitative Theory of Second Order Dynamical Systems, John Wiley & Sons, New York, 1973. | MR | Zbl
et al.,[C] A survey of Quadratic Systems, Journal of Differential Equations, 2 (1966), 293-304. | MR | Zbl
,[Ca] Applications of Center Manifold Theory, Applied Math. Sciences, 35, Springer-Verlag, 1981. | MR | Zbl
,[Ch-S] Separatrix and Limit Cycles of Quadratic Systems and Dulac's Theorem, Transactions Amer. Math. Soc., 278 (1983), 585-612. | MR | Zbl
and ,[D] Sur les cycles limites, Bull. Soc. Math. France, 51 (1923), 45-188. | JFM | Numdam
,[Du] Singularities of Vector Fields, Journal of Differential Equations, 23, I (1977), 53-106. | MR | Zbl
,[H-P-S] Invariant Manifolds, Springer Lecture Notes in Math., 583 (1977). | MR | Zbl
, and ,[I] 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] 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
and ,[P-L2] 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
and ,[P-L3] 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
and ,[P-M] Geometric Theory of Dynamical Systems ; An Introduction, New York, Springer-Verlag, 1982. | MR | Zbl
and ,[S] Curvas definidas por equaçoes diferenciais no plano, 13° Colóquio Bras. de Mat., IMPA, 1981. | MR
,[Sh1] 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] A method for constructing cycles without contact around a weak focus, Journal of Differential Equations, 41 (1981), 301-312. | MR | Zbl
,