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

Authors: Colin Christopher and Jaume Llibre
Journal: Proc. Amer. Math. Soc. 130 (2002), 2025-2030
MSC (2000): Primary 34C05, 34A34, 34C14
Published electronically: December 27, 2001
MathSciNet review: 1896037
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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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Additional Information

Colin Christopher
Affiliation: School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon PL4 8AA, United Kingdom

Jaume Llibre
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

Keywords: Rational first integral, invariant algebraic curve, quadratic systems
Received by editor(s): November 1, 2000
Received by editor(s) in revised form: January 25, 2001
Published electronically: December 27, 2001
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2001 American Mathematical Society