Melnikov functions and perturbation of a planar Hamiltonian system

Chinese Annals of Mathematics. Series B

Volumn 20, Issue 2, 1999, Pages 233-246

  Jiang, Qibao ^a   Han, Mao'an ^b  

^a SOUTHEAST UNIVERSITY   (China)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Bifurcation; Limit cycles; Melnikov functions

Indexed keywords

EID: 0033413671     PISSN: 02529599     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0252959999000266     Document Type: Article

References (10)

1. Arnold, V. I., Gusein-Zade, S. M. & Varchenko, A. N., Singularities of differentiate maps (vol.II), Birkhäuser, 1988.
2. Han Mao'an, Bifurcation of limit cycles and the cusp of order N, Acta Math. Sinica, New Series, 13:1 (1997), 64-75.
3. Han Mao'an, On the number of limit cycles bifurcation from a homoclinic or heteroclinic loop, Science in China, 2(1992), 113-122.
4. w, where R(z, w) is a polynomial Mat. Sb., 78(1969), 360-373 (in Russian).
5. Li Chengzhi, Llibre, J. & Zhang Zhifen, Abelian integral of quadratic Hamiltonian vector field with an invariant line, Preprint, 1993.
6. Li Baoyi & Zhang Zhifen, A note on a G.S. Petrov's result about the weakened 16th Hubert problem, J. Math. Anal. Appl. 190(1995), 489-516.
7. Li Baoyi & Zhang Zhifen, High order Melnikov functions and problem of uniformity in global bifurcation, Annali di Mat. Pura and Appl. CLXI(1992), 181-212.
8. Roussarie, R., On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields, Bol. Soc. Brasil. Mat. 17(1986), 67-101.
9. Ye Yanqian et al, Theory of limit cycles, Trans. of Math. Monograph, vol.66, AMS, 1986.
10. Jiang, Q. & Han, M., Melnikov functions and perturbation of a planar Hamiltonian system, Preprint of Centre de Recerca Matematica, No.310, 1995.