Invariant algebraic curves linear in one variable for planar real quadratic systems. (Q1406140)
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scientific article; zbMATH DE number 1978003
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariant algebraic curves linear in one variable for planar real quadratic systems. |
scientific article; zbMATH DE number 1978003 |
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Invariant algebraic curves linear in one variable for planar real quadratic systems. (English)
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9 September 2003
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The paper is devoted to the study of algebraic solutions in the form \(h(x,y)=p_1(x)y+p_2(x)\), where \(p_1(x)\neq 0\) and \(p_2(x)\) are real coprime polynomials, for a real autonomus quadratic system in the plane. The authors classify all possible solutions of this type for such system in terms of the coefficients of the system. An explicit system with an invariant quartic is given.
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invariant algebraic curve
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quadratic polynomial differential systems
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rational curve
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