2007, Vol.10, No.1, pp.79-85
We give a simple proof of Bautin's theorem on the cyclicity of
the quadratic system of differential equations [2]. The proof is based on elementary algorithms of computational algebra. Namely, we show that the variety of the Bautin ideal
coincides with the variety of the ideal generated
by the first three focus quantities and the ideal
is a radical one. This yields a bound for the cyclicity obtained
by Bautin.
Key words:
limit cycles, cyclicity, center problem
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