A criterion for determining the monotonicity of the ratio of two Abelian integrals

Journal of Differential Equations

Volumn 124, Issue 2, 1996, Pages 407-424

  Li, Chengzhi ^a   Zhang, Zhi Fen ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001686233     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0017     Document Type: Article

References (14)

1. V. I. ARNOLD, "Geometrical Methods in the Theory of Ordinary Differential Equations," Springer-Verlag, New York, 1983.
2. J. A. SANDERS AND R. CUSHMAN, Abelian integrals and global Hopf bifurcations, Springer Lecture Notes in Math. 1125 (1985), 87-98.
3. R. CUSHMAN AND J. A. SANDERS, A codimension two bifurcation with a third order Picard-Fuchs equation, J. Differential Equations 59 (1985), 243-256.
4. S.-N. CHOW, C. LI, AND D. WANG, Uniqueness of periodic orbits in some vector fields with codimension two singularities, J. Differential Equations 77 (1989), 231-253.
5. H. ZOLADEK, Quadratic systems with center and their perturbations, preprint, 1990.
6. A. I. NEISHTADT, Bifurcations of phase portrait of certain system of equations arising in the problem of loss of selfoscillations near resonance 1:4, Prikl. Mat. Mech. 42, No. 5 (1978), 896-907.
7. H. ZOLADEK, Abelian integrals in unfoldings of codimension 3 singular planar vector fields, Springer Lecture Notes in Math. 1480 (1991), 165-224
8. Z.-F. ZHANG AND C. LI, On the number of limit cycles of a class of quadratic hamiltonian systems under quadratic perturbations, preprint, 1993.
9. Y. HUE AND C. LI, On the number of limit cycles arising from perturbations of a homoclinic loop of quadratic integrable systems, preprint, 1993.
10. R. I. BOGDANOV, Versal deformations of a singularity of a vector field on the plane in the case of zero eigenvalues, Proc. Petrovski Sem. 2 (1976), 37-65.
11. F. TAKENS, Forced oscillations and bifurcations in applications of global analysis I, Comm. Math. Inst. Rijksuniversiteit Utrecht (1974), 1-59.
12. H. ZOLADEK, On versality of certain family of symmetric vector fields on the plane, Math. Sborn. 48, No. 2 (1984), 463-492.
13. J. CARR, S.-N. CHOW, AND J. K. HALE, Abelian integrals and bifurcation theory, J. Differential Equations 59 (1985), 413-436.
14. B. DRACHMAN, S. A. VAN GILS, AND Z. F. ZHANG, Abelian integrals for quadratic vector fields, J. Reine Angew. Math. 382 (1987), 165-180.