A family of non-Darboux-integrable quadratic polynomial differential systems with algebraic solutions of arbitrarily high degree (Q1431824)
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scientific article; zbMATH DE number 2073692
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A family of non-Darboux-integrable quadratic polynomial differential systems with algebraic solutions of arbitrarily high degree |
scientific article; zbMATH DE number 2073692 |
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A family of non-Darboux-integrable quadratic polynomial differential systems with algebraic solutions of arbitrarily high degree (English)
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11 June 2004
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The authors find a new counterexample to the conjecture given by Lins-Neto. They prove that the system \(\dot x=1,\dot y =2n + 2xy + y^2\) has a unique irreducible invariant algebraic curve, but the system has neither a Darboux first integral, nor a Darboux integration factor.
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