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

Christopher, Colin; Llibre, Jaume

doi:10.1090/S0002-9939-01-06253-0

A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals
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by Colin Christopher and Jaume Llibre PDF

Proc. Amer. Math. Soc. 130 (2002), 2025-2030 Request permission

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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