Finite cyclicity of nilpotent graphics of pp-type surrounding a center
Roussarie, R. ; Rousseau, C.
Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, p. 889-920 / Harvested from Project Euclid
This paper is part of the DRR-program of [4] to prove the finiteness part of Hilbert's 16th problem for quadratic vector fields by showing the finite cyclicity of 121 graphics. In this paper we prove the finite cyclicity of 4 graphics passing through a triple nilpotent point of elliptic type surrounding a center, namely the graphics $(H_7^1)$, $(F_{7a}^1)$, $(H_{11}^3)$ and $(I_{6a}^1)$. These four graphics are of pp-type, in the sense that they join two parabolic sectors of the nilpotent point. The exact cyclicity is 2 for $(H_7^1)$ and $(H_{11}^3)$. The graphics $(F_{7a}^1)$ and $(I_{6a}^1)$ occur in continuous families. Their exact cyclicity is 2 except for a discrete subset of such graphics. The method can be applied to most other graphics of the DRR-program [4] through a triple nilpotent point and surrounding a center.
Publié le : 2008-11-15
Classification: 
@article{1228486414,
     author = {Roussarie, R. and Rousseau, C.},
     title = {Finite cyclicity of nilpotent graphics of pp-type surrounding a center},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 889-920},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1228486414}
}
Roussarie, R.; Rousseau, C. Finite cyclicity of nilpotent graphics of pp-type surrounding a center. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp.  889-920. http://gdmltest.u-ga.fr/item/1228486414/