Linear estimation of the number of zeros of Abelian integrals for some cubic isochronous centers

Journal of Differential Equations

Volumn 180, Issue 2, 2002, Pages 307-333

  Li, Chengzhi ^a   Li, Weigu ^a   Llibre, Jaume ^b   Zhang, Zhifen ^a  

^a PEKING UNIVERSITY   (China)

^b UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037052007     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2001.4064     Document Type: Article

References (26)

1. Bifurcation of limit cycles from centers and separatrix cycles of planar analytic systems
2. Bifurcation of limit cycles from quadratic isochronous
3. Integrability via invariant algebraic curves for planar polynomial differential systems
4. Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops
5. Modules of Abelian integrals
6. On the nonexistence, existence, and uniqueness of limit cycles
7. On the shape of limit cycles that bifurcate from Hamiltonian centers
8. The shape of limit cycles that bifurcate from non-Hamiltonian centers
9. On the number of limit cycles in perturbations of quadratic Hamiltonian systems
10. Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
11. Perturbations of quadratic centers
12. On the limit cycles of polynomial differential systems with homogeneous nonlinearities
13. Linear estimate for the number of zeros of Abelian integrals for quadratic isochronous centers
14. A note on a result of G.S. Petrov about the weakened 16th Hilbert problem
15. Averaging analysis of a perturbed quadratic center
16. Double exponential estiamte for the number of zeros of complete Abelian integrals and rational envelopes of linear ordinary differential equations with an irreducible monodromy group
17. Behavior of the period of solutions of certain plane autonomous system near centers
18. The number of limit cycles of polynomials deformations of a Hamiltonian vector field
19. Linearization of isochronous centers
20. Simple exponential estimate for the number of real zeros of complete Abelian integrals
21. Number of zeros of complete elliptic integrals
22. Nonoscillation of elliptic integrals
23. Bifurcation of limit cycles from quadratic centers
24. On functions (and curves) defined by differential equations
25. Quadratic systems with centers and their perturbations