메뉴 건너뛰기




Volumn 29, Issue 7, 1997, Pages 783-811

Phase portraits of planar semi-homogeneous vector fields - I

Author keywords

Phase portraits; Semi homogeneous systems

Indexed keywords

EQUIVALENCE CLASSES; NONLINEAR EQUATIONS; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING; TOPOLOGY;

EID: 0031258109     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00088-0     Document Type: Article
Times cited : (27)

References (33)
  • 1
  • 2
    • 0001537866 scopus 로고
    • Quadratic differential equations and non-associative algebras
    • Princeton University Press
    • Markus, L., Quadratic differential equations and non-associative algebras. In Annals of Mathematics Studies, Vol. 45. Princeton University Press, 1960, pp. 185-213.
    • (1960) Annals of Mathematics Studies , vol.45 , pp. 185-213
    • Markus, L.1
  • 4
    • 0007438921 scopus 로고
    • Geometric classification of quadratic differential systems
    • Sibirskii, K. S. and Vulpe, N. I., Geometric classification of quadratic differential systems. Differential Equations, 1977, 13, 548-556.
    • (1977) Differential Equations , vol.13 , pp. 548-556
    • Sibirskii, K.S.1    Vulpe, N.I.2
  • 5
    • 0001321275 scopus 로고
    • Two-dimensional homogeneous quadratic differential systems
    • Newton, T. A., Two-dimensional homogeneous quadratic differential systems. SIAM Review, 1978, 20, 120-138.
    • (1978) SIAM Review , vol.20 , pp. 120-138
    • Newton, T.A.1
  • 6
    • 0001903255 scopus 로고
    • Classification and analysis of two-dimensional homogeneous quadratic differential equations systems
    • Date, T., Classification and analysis of two-dimensional homogeneous quadratic differential equations systems. J. diff. Eqns, 1979, 32, 311-334.
    • (1979) J. Diff. Eqns , vol.32 , pp. 311-334
    • Date, T.1
  • 7
    • 0040548092 scopus 로고
    • 2) by Forster's method
    • 2) by Forster's method (in Russian). Diff. Uravn., 1984, 20, 1809-1813.
    • (1984) Diff. Uravn. , vol.20 , pp. 1809-1813
    • Vdovina, E.V.1
  • 8
    • 38249020465 scopus 로고
    • Algebraic and topological classification of the homogeneous cubic vector fields in the plane
    • Cima, A. and Llibre, J., Algebraic and topological classification of the homogeneous cubic vector fields in the plane. J. math. Analysis Applic., 1990, 147, 420-448.
    • (1990) J. Math. Analysis Applic. , vol.147 , pp. 420-448
    • Cima, A.1    Llibre, J.2
  • 13
    • 0000149382 scopus 로고
    • Bounded quadratic systems in the plane
    • Dickson, R. J. and Perko, L. M., Bounded quadratic systems in the plane. J. diff. Eqns, 1970, 6, 251-273.
    • (1970) J. Diff. Eqns , vol.6 , pp. 251-273
    • Dickson, R.J.1    Perko, L.M.2
  • 14
    • 38249033158 scopus 로고
    • Some theorems on the existence, uniqueness and nonexistence of limit cycles for quadratic systems
    • Coll, B., Gasull, A. and Llibre, J., Some theorems on the existence, uniqueness and nonexistence of limit cycles for quadratic systems. J. diff. Eqns, 1987, 67, 372-399.
    • (1987) J. Diff. Eqns , vol.67 , pp. 372-399
    • Coll, B.1    Gasull, A.2    Llibre, J.3
  • 17
    • 84968466565 scopus 로고
    • On the nonsingular quadratic differential equations in the plane
    • Gasull, A. and Llibre, J., On the nonsingular quadratic differential equations in the plane. Proc. Am. math. Soc., 1988, 104, 793-794.
    • (1988) Proc. Am. Math. Soc. , vol.104 , pp. 793-794
    • Gasull, A.1    Llibre, J.2
  • 21
    • 43949147636 scopus 로고
    • Hamiltonian quadratic systems
    • Artés, J. C. and Llibre, J., Hamiltonian quadratic systems. J. diff. Eqns, 1994, 107, 80-95.
    • (1994) J. Diff. Eqns , vol.107 , pp. 80-95
    • Artés, J.C.1    Llibre, J.2
  • 23
    • 21844526553 scopus 로고
    • Phase portraits for quadratic systems having a focus and one antisaddle
    • Artés, J. C. and Llibre, J., Phase portraits for quadratic systems having a focus and one antisaddle. Rocky Mount. J. Math., 1994, 24, 875-889.
    • (1994) Rocky Mount. J. Math. , vol.24 , pp. 875-889
    • Artés, J.C.1    Llibre, J.2
  • 25
    • 0007075672 scopus 로고
    • Affine-invariant conditions for the topological discrimination of quadratic systems with a center
    • Vulpe, N. I., Affine-invariant conditions for the topological discrimination of quadratic systems with a center. Differential Equations, 1983, 19, 273-280.
    • (1983) Differential Equations , vol.19 , pp. 273-280
    • Vulpe, N.I.1
  • 26
    • 0009367660 scopus 로고
    • Integrals of a general quadratic differential system in cases of a center
    • Lunkevich, V. A. and Sibirskii, K. S., Integrals of a general quadratic differential system in cases of a center. Differential Equations, 1982, 18, 563-568.
    • (1982) Differential Equations , vol.18 , pp. 563-568
    • Lunkevich, V.A.1    Sibirskii, K.S.2
  • 28
    • 0000449178 scopus 로고
    • Investigation of the behaviour of the integral curves of a system of two differential equations in the neighborhood of a singular point
    • Andreev, A. F., Investigation of the behaviour of the integral curves of a system of two differential equations in the neighborhood of a singular point. Trans. Am. math. Soc., 1958, 8, 183-207.
    • (1958) Trans. Am. Math. Soc. , vol.8 , pp. 183-207
    • Andreev, A.F.1
  • 29
    • 0003318109 scopus 로고
    • Dynamical systems - I, Ordinary differential equations
    • Springer, Heidelberg
    • Arnold, V. I. and Ilyashenko, Y. S., Dynamical systems - I, Ordinary differential equations. In Encyclopaedia of Mathematical Sciences, Vols 1-2. Springer, Heidelberg 1988.
    • (1988) Encyclopaedia of Mathematical Sciences , vol.1-2
    • Arnold, V.I.1    Ilyashenko, Y.S.2
  • 30
    • 0001328254 scopus 로고
    • Generic properties of polynomial vector fields at infinity
    • Gonzalez, E. A., Generic properties of polynomial vector fields at infinity. Trans. Am. math. Soc., 1969, 143, 201-22.
    • (1969) Trans. Am. Math. Soc. , vol.143 , pp. 201-222
    • Gonzalez, E.A.1
  • 31
    • 0003264465 scopus 로고
    • Theory of Limit Cycles
    • American Mathematical Society, Providence, RI
    • Ye Yanqian, Theory of Limit Cycles. Translations of Math. Monographs, Vol. 66. American Mathematical Society, Providence, RI, 1986.
    • (1986) Math. Monographs , vol.66
    • Ye, Y.1
  • 32
    • 0001520664 scopus 로고
    • A survey of quadratic systems
    • Coppel, W. A., A survey of quadratic systems. J. diff. Eqns, 1962, 2, 293-304.
    • (1962) J. Diff. Eqns , vol.2 , pp. 293-304
    • Coppel, W.A.1
  • 33
    • 84968503704 scopus 로고
    • Classification of continuous flows on 2-manifolds
    • Neumann, D., Classification of continuous flows on 2-manifolds. Proc. Am. math. Soc., 1975, 48, 73-81.
    • (1975) Proc. Am. Math. Soc. , vol.48 , pp. 73-81
    • Neumann, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.