Bautin ideal of a cubic map (Q5938896)
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scientific article; zbMATH DE number 1631112
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bautin ideal of a cubic map |
scientific article; zbMATH DE number 1631112 |
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Bautin ideal of a cubic map (English)
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7 August 2001
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cubic polynomials
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Bautin ideal
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center variety
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The authors deal with the cubic polynomial of the form NEWLINE\[NEWLINE\psi(z,w)= z+w+Az^2+ Bzw+ Cw^2+ Dz^3+ Ez^2w+ Fzw^2+ Gw^3, \tag{1}NEWLINE\]NEWLINE where \(A,B,\dots, G\in \mathbb{C}\). The main goal of the paper is to show that the ideal \(I_3\) defining the center variety of polynomial (8) is not radical, and therefore, it is impossible to give an estimation for cyclicity of centers defined by polynomial (1) by directly applying well-known Bautin's method.
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