Perturbation from a cubic Hamiltonian with three figure eight-loops

Chaos, Solitons and Fractals

Volumn 22, Issue 1, 2004, Pages 61-74

  Hong, Zang ^a,b   Chen, Wencheng ^b   Tonghua, Zhang ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; BIFURCATION (MATHEMATICS); FUNCTIONS; PERTURBATION TECHNIQUES; POLYNOMIALS; VECTORS;

CUBIC SYSTEMS; MELNIKOV FUNCTIONS;

HAMILTONIANS;

EID: 1842528979     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2003.12.061     Document Type: Article

References (15)

1. Han M. Cyclicity of planar homoclinic loops and quadratic integrable systems. Sci. China, Ser. A. 40(12):1997;1247-1258.
2. Han M., Chen J. On the number of limit cycles in double homoclinic bifurcations. Sci. China, Ser. A. 43(9):2000;914-928.
3. Han M., Hu S., Liu X. On the stability of double homoclinic and heteroclinic cycles. Nonlinear Anal. 53:2003;701-713.
4. 2 -equivariant cubic perturbation. Int J Bifurcat & Chaos [in press].
5. Han M, Zhang T, Zang H. On the number and distributions of limit cycles in a cubic system. Int J Bifurcat & Chaos [in press].
6. 3 -equivariant vector field of degree 5 Int. J. Bifurcat & Chaos. 11(8):2001;2287-2298.
7. Li J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields. Int. J. Bifurcat. & Chaos. 13(1):2003;47-106.
8. Li J., Huang Q. Bifurcations of limit cycles forming compound eyes in the cubic system. Chinese Ann. Math. 8B(4):1987;391-403.
9. 2 -equivariant planar vector fields of degree 5 Int. J. Bifurcat. & Chaos. 12(10):2002;2137-2157.
10. Li J., Liu Z. Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system. Publ. Math. 35:1991;487-506.
11. Liu Z., Yang Z., Jiang T. The same distribution of limit cycles in five perturbed cubic Hamiltonian systems. Int. J. Bifurcat. & Chaos. 13(1):2003;243-249.
12. Smale S. Mathematical problems for the next century. The Mathematical Intelligence. 20(2):1998;7-15.
13. Ye Y. Theory of limit cycles. Transactions of Mathematical Monographs. vol. 66:1986;American Mathematical Society, Boston.
14. Ilyashenko Yu. Finiteness Theorem for Limit Cycles. 1991;American Mathematical Society, Providence, RI.
15. Zhang T., Zang H., Han M. Bifurcations of limit cycles in a cubic system. Chaos, Solitons & Fractals. 20:2004;629-638.