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Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
(Journal of Differential Equations (Elsevier Science), 2002)
In this paper we prove finite cyclicity of several of the most generic graphics through a nilpotent point of saddle or elliptic type of codimension 3 inside C . families of planar vector fields. In some cases our results ...
PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert's 16th problem
(Journal of Differential Equations (Elsevier Science), 2004)
This paper is part of the program launched in (J. Differential Equations 110(1) (1994) 86) to prove the finiteness part of Hilbert’s 16th problem for quadratic system, which consists in proving that 121 graphics have finite ...