메뉴 건너뛰기




Volumn 246, Issue 8, 2009, Pages 3361-3379

On the focus order of planar polynomial differential equations

Author keywords

Center focus; Focus order; Lyapunov constants; Polynomial systems

Indexed keywords


EID: 61849151338     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2009.02.005     Document Type: Article
Times cited : (9)

References (13)
  • 2
    • 0000495631 scopus 로고
    • On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type
    • English transl. in:
    • Bautin N.N. On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type. Mat. Sb. 30 (1952) 181-196 English transl. in:
    • (1952) Mat. Sb. , vol.30 , pp. 181-196
    • Bautin, N.N.1
  • 3
    • 0000465791 scopus 로고
    • On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type
    • Bautin N.N. On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type. Math. USSR Sb. 100 (1954) 397-413
    • (1954) Math. USSR Sb. , vol.100 , pp. 397-413
    • Bautin, N.N.1
  • 5
    • 0030546995 scopus 로고    scopus 로고
    • Successive derivatives of a first return map, application to the study of quadratic vector fields
    • Françoise J.P. Successive derivatives of a first return map, application to the study of quadratic vector fields. Ergodic Theory Dynam. Systems 16 (1996) 87-96
    • (1996) Ergodic Theory Dynam. Systems , vol.16 , pp. 87-96
    • Françoise, J.P.1
  • 6
    • 0018530408 scopus 로고
    • Lyapunov approach to multiple Hopf bifurcation
    • Gobber F., and Willamowskii K.D. Lyapunov approach to multiple Hopf bifurcation. J. Math. Anal. Appl. 71 (1979) 333-350
    • (1979) J. Math. Anal. Appl. , vol.71 , pp. 333-350
    • Gobber, F.1    Willamowskii, K.D.2
  • 8
    • 41149174316 scopus 로고    scopus 로고
    • A quartic system and a quintic system with fine focus of order 18
    • Huang J., Wang F., Wang L., and Yang J. A quartic system and a quintic system with fine focus of order 18. Bull. Sci. Math. 132 3 (2008) 205-217
    • (2008) Bull. Sci. Math. , vol.132 , Issue.3 , pp. 205-217
    • Huang, J.1    Wang, F.2    Wang, L.3    Yang, J.4
  • 9
    • 0037246396 scopus 로고    scopus 로고
    • Hilbert's 16th problem and bifurcations of planar polynomial vector fields
    • Li J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields. Inernat. J. Bifur. Chaos 13 (2003) 47-106
    • (2003) Inernat. J. Bifur. Chaos , vol.13 , pp. 47-106
    • Li, J.1
  • 10
    • 70350376754 scopus 로고    scopus 로고
    • J. Llibre, Integrability of polynomial differential systems, in: Handbook of Differential Equations (Ordinary Differential Equations, 1), Elsevier, North-Holland, 2004, pp. 437-532
    • J. Llibre, Integrability of polynomial differential systems, in: Handbook of Differential Equations (Ordinary Differential Equations, vol. 1), Elsevier, North-Holland, 2004, pp. 437-532
  • 11
    • 0001304970 scopus 로고
    • Algebraic and geometric aspects of the theory of polynomial vector fields
    • Bifurcations and Periodic Orbits of Vector Fields. Schlomiuk D. (Ed), Kluwer Academic, London
    • Schlomiuk D. Algebraic and geometric aspects of the theory of polynomial vector fields. In: Schlomiuk D. (Ed). Bifurcations and Periodic Orbits of Vector Fields. NATO ASI Ser. C vol. 408 (1993), Kluwer Academic, London 429-467
    • (1993) NATO ASI Ser. C , vol.408 , pp. 429-467
    • Schlomiuk, D.1
  • 12
    • 0002754080 scopus 로고
    • The number of limit cycles in the neighborhood of a singular point
    • Sibirskii K.S. The number of limit cycles in the neighborhood of a singular point. Differential Equations 1 (1965) 36-47
    • (1965) Differential Equations , vol.1 , pp. 36-47
    • Sibirskii, K.S.1
  • 13
    • 0000113158 scopus 로고
    • Eleven small limit cycles in a cubic vector field
    • Zoladek H. Eleven small limit cycles in a cubic vector field. Nonlinearity 8 (1995) 843-860
    • (1995) Nonlinearity , vol.8 , pp. 843-860
    • Zoladek, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.