PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert's 16th problem

Journal of Differential Equations

Volumn 196, Issue 1, 2004, Pages 169-208

  Rousseau, Christiane ^a   Zhu, Huaiping ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b YORK UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347031469     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00119-0     Document Type: Article

References (13)

1. F. Dumortier, M.El. Morsalani, C. Rousseau, Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics, Nonlinearity 9 (5) (1996) 1209-1261.
2. F. Dumortier, A. Guzmán, C. Rousseau, Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems, Qualitative Theory Dyn. Systems 3 (2002) 123-154.
3. F. Dumortier, Y. Ilyashenko, C. Rousseau, Normal forms near a saddle-node and applications to finite cyclicity of graphics, Ergodic Theory Dynamical Systems 22 (2002) 783-818.
4. F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1) (1994) 86-133.
5. F. Dumortier, R. Roussarie, C. Rousseau, Elementary graphics of cyclicity 1 and 2, Nonlinearity 7 (3) (1994) 1001-1043.
6. F. Dumortier, R. Roussarie, S. Sotomayor, Generic 3-parameter Families of Vector Fields in the Plane, Unfoldings of Saddle, Focus and Elliptic Singularities with Nilpotent Linear Parts, in: Y. Ilashenko, S. Yakovenko (Eds.), Lecture Notes in Mathematics, Vol. 1480, Springer, Berlin, 1991, pp. 1-164.
7. F. Dumortier, R. Roussarie, S. Sotomayor, Bifurcations of cuspidal loops, Nonlinearity 10 (6) (1997) 1369-1408.
8. A. Guzmán, C. Rousseau, Genericity conditions for finite cyclicity of elementary graphics, J. Differential Equations 155 (1) (1999) 44-72.
9. Y. Ilyashenko, S. Yakovenko, Finite-smooth normal forms of local families of diffeomorphisms and vector fields, Russian Math. Surveys 46 (1991) 1-43.
10. A. Kotova, V. Stanzo, On few-parameter generic families of vector fields on the two-dimensional sphere, in: Concerning the Hilbert 16th problem, American Mathematical Society Translation Series 2, Vol. 165, American Mathematical Society, Providence, RI, 1995, pp. 155-201.
11. A. Mourtada, Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan: mise sous forme normale, in: Bifurcations of Planar Vector Fields (Luminy, 1989), Lecture Notes in Mathematics, Vol. 1455, Springer, Berlin, 1990, pp. 272-314.
12. S. Sternberg, On the structure of local homeomorphisms of euclidean n-space. II, Amer. J. Math. 80 (1958) 623-631.
13. H. Zhu, C. Rousseau, Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type, J. Differential Equations 178 (2) (2002) 325-436.