Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type

Journal of Differential Equations

Volumn 178, Issue 2, 2002, Pages 325-436

  Zhu, Huaiping ^a   Rousseau, Christiane ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037137987     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2001.4017     Document Type: Article

References (38)

1. "Ordinary Differential Equations"
2. "Theory of Bifurcations of Dynamical Systems on a Plane"
3. Conjugacy of vector fields respecting additional properties
4. Singularities of vector fields on the plane
5. "Singularities of Vector Fields"
6. Techniques in the theory of local bifurcations: Blow-up, normal forms, nilpotent bifurcations, singular perturbations
7. Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics
8. Normal forms near a saddle node and applications to finite cyclicity of graphics
9. Cubic Liénard equations with linear damping
10. Canard cycles and center manifolds (with an appendix by Chengzhi Li)
11. Hilbert's 16th problem for quadratic vector fields
12. Elementary graphics of cyclicity 1 and 2
13. "Generic 3-parameter Families of Vector Fields in the Plane, Unfoldings of Saddle, Focus and Elliptic Singularities with Nilpotent Linear Parts"
14. Bifurcations of cuspidal loops
15. Perturbations of graphics with semihyperbolic singularities
16. "Non-linear Oscillations, Dynamical Systems and Bifurcation of Vector fields"
17. Genericity conditions for finite cyclicity of elementary graphics
18. Finiteness theorems for limit cycles
19. "Nonlinear Stokes Phenomena"
20. Finite-smooth normal forms of local families of diffeomorphisms and vector fields
21. Concerning the Hilbert sixteenth Problem
22. Finite cyclicity of elementary polycycles in generic families
23. Saddle quantities and applications
24. On few-parameter generic families of vector fields on the two-dimensional sphere
25. On the generation of limit cycle from separatrice
26. Problèmes de modules pour des équations différentielles non linéaires du premier ordre
27. Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan: Mise sous forme normale
28. Degenerate and non-trivial hyperbolic polycycles with two vertices
29. "Projection de sous-ensembles quasi-réguliers de Dulac-Hilbert. Un cas noethérien"
30. A note on finite cyclicity property and Hilbert's 16th problem
31. On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
32. "Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem"
33. Hilbert's 16th problem for quadratic systems and finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
34. Bifurcations of polynomial vector fields in the plane
35. On the structure of local homeomorphisms of euclidean n-space, II
36. Unfoldings of certain singularities of vector fields: Generalized Hopf bifurcations
37. Singularities of vector fields
38. "Finite Cyclicity of Graphics with a Nilpotent Singularity of Saddle or Elliptic Type"