A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals

Christopher C.; Llibre J.

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A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals

机译：一族具有任意高阶不变代数曲线的二次多项式微分系统，而没有有理第一积分

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We give a class of quadratic systems without rational first integral which contains irreducible algebraic solutions of arbitrarily high degree. The construction gives a negative answer to a conjecture of Lins Neto and others. [References: 20]

机译：我们给出了一类没有有理第一积分的二次系统，它包含任意高阶的不可约代数解。这种构造对林斯·内图和其他人的猜想给出了否定的答案。 [参考：20]

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《Proceedings of the American Mathematical Society》 |2002年第7期|共6页
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Christopher C.; Llibre J.;
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正文语种 eng
中图分类数学;
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6. Integral-valued polynomials over sets of algebraic integers of bounded degree [O] . Giulio Peruginelli -1

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7. A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals [O] . Colin Christopher, Jaume Llibre 2001

机译：一系列二次多项式差动系统，具有不良高度的不变代数曲线，无需合理的第一积分

A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals

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