Jumping property of Lyapunov values

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 39, Issue 12, 1996, Pages

  Mao, Rui ^a   Wang, Duo ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Lyapunov value; Planar polynomial systems; Weak focus

Indexed keywords

EID: 0012880132     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Lyapunov, A. M., General Problem of Stability of Motion, Moscow: Gos. Izd. Tekh-Teor. Lit., 1950.
2. Far, W. W., Li, C., Labouriau, I. S. et al., Degenerate Hopf bifurcation formulas and Hubert's 16-th problem, SIAM J. Math. Anal., 1989, 20(1):13.
3. Andronov, A. A., Gordon, I. I., Leontvich., E. A. et al., Theory of Bifurcations of Dynamical Systems on a Plane, New York: John Wiley, 1973.
4. Chow, S., Li, C., Wang, D., Normal Forms and Bifurcation of Planar Vector Fields, London: Cambridge University Press, 1994.
5. Nemytskii, V. V., Stepanov, V. V., Qualitative Theory of Differential Equations, Princeton: Princeton University Press, 1960.
6. Bonin, G., Legault, J., Comparison de la méthode des constants de Lyapunov et la bifurcation de Hopf, Canad. Math. Bull., 1988, 31(2):200.
7. Zhang, Z., Ding, T., Huang, W. et al., Qualitative Theory of Differential Equations (in Chinese), Beijing: Science Press, 1985.
8. Wang, D., Mao, R., A complex algorithm for computing Lyapunov values, Random & Computational Dynamics, 1994, 2(3 & 4):261.
9. Poincaré, H., Mémoire sur les courbes définies par les équations différentielles, J. Math. Pures. Appl., 1885, 1(4): 167.
10. Shi, S., On the structure of Poincaré-Lyapunov coastants for the weak focus of 'polynomial vector fields, J. D. E., 1984, 52:52.
11. Anosov, D. V., Arnold, V. I., Dynamical System I, Berlin: Springer-Verlag, 1990.
12. Bautin, N. N., On the number of limit cycles which appear with the variation of coefficients from an equilibrium point of focus or center type, AMS Tran. Series I. V., 1962, 5:396. (Russian original: Math. Sbornik, 1952, 30:181.)
13. Bautin, N. N., On the number of limit cycles which appear with the variation of coefficients from an equilibrium point of focus or center type, AMS Tran. Series I. V., 1962, 5:396. (Russian original: Math. Sbornik, 1952, 30:181.)
14. Sibirskii, K. S., On the number of limit cycles in a neighborhood of singular points. Diff. Eqs., 1965, 1:36.
15. Wang, D., A recursive formula and its applications to computations of normal forms and focal values, in Dynamical System (eds. Liao, S. T., Ye, Y. Q., Ding, T. R.), Singapore: World Scientific, 1993, 238-247.
16. Liu, Y., Li, J., Theory of values of singular point in complex autonomous differential systems, Science in China, Ser. A, 1990, 33(1):10.
17. Lloyd, N. G., The number of limit cycles of polynomial systems in the plane. Bull. Inst. Math. Appl., 1988, 24:161.