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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Email: cchristopher@plymouth.ac.uk

Jaume Llibre
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
Email: jllibre@mat.uab.es

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06253-0
PII: S 0002-9939(01)06253-0
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