A unified proof of the weakened Hilbert 16th problem for \(n=2\) (Q817590)
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scientific article; zbMATH DE number 5012952
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A unified proof of the weakened Hilbert 16th problem for \(n=2\) |
scientific article; zbMATH DE number 5012952 |
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A unified proof of the weakened Hilbert 16th problem for \(n=2\) (English)
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16 March 2006
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The paper focuses on the weakened Hilbert's 16th problem which is closely related to the least upper bound of the number of zeros \(Z(n)\) of the Abelian integral, where \(n\) is the degree of the corresponding polynomial perturbed Hamiltonian system. It is known that for \(n=2\) this problem was completely solved (\(Z(2)=2\)) by using different methods for different cases. Therefore, the authors present a unified approach for all cases restricted to the real domain, combining geometric and analytical methods.
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Hamiltonian system
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limit cycle
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weak Hilbert's 16th problem
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Abelian integral
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centroid curve
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deformation argument
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