Proceedings of the American Mathematical Society

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

Author(s): Colin Christopher; Jaume Llibre
Journal: Proc. Amer. Math. Soc. 130 (2002), 2025-2030.
MSC (2000): Primary 34C05, 34A34, 34C14
Posted: December 27, 2001
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Abstract: 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.

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Colin Christopher
Affiliation: School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon PL4 8AA, United Kingdom
Email: cchristopher@plymouth.ac.uk

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ISSN 1088-6826 (e) ISSN 0002-9939 (p)

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