The infinitesimal 16th Hilbert problem in the quadratic case |
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| Authors: | Lubomir Gavrilov |
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| Institution: | (1) Laboratoire Emile Picard, UMR 5580, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France (e-mail: gavrilov@picard.ups-tlse.fr), FR |
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| Abstract: | Let H(x,y) be a real cubic polynomial with four distinct critical values (in a complex domain) and let X
H
=H
y
-H
x
be the corresponding Hamiltonian vector field. We show that there is a neighborhood ? of X
H
in the space of all quadratic plane vector fields, such that any X∈? has at most two limit cycles.
Oblatum 23-III-2000 & 19-VI-2000?Published online: 11 October 2000 |
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| Keywords: | |
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