Bautin ideal of a cubic map
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We compute the radical of the ideal generated by the first three focus quantities of maps defined by irreducible branches of a cubic curve on the real plane. It is shown that the ideal is not radical in this case.
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Benediktovitch, I. Bautin ideal of a cubic map / I. Benediktovitch, V. Romanovski // Applied Mathematics Letters. – 2001. – Vol. 14, № 2. – P. 159-165.