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A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals |
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| Authors: | Colin Christopher Jaume Llibre |
| Affiliation: | School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon PL4 8AA, United Kingdom ; Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain |
| 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. |
| Keywords: | Rational first integral invariant algebraic curve quadratic systems |
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