Resumen de On a counterexample of Lins-Neto conjecture

Javier Chavarriga Soriano , Maite Grau Montaña

• We study invariant algebraic curves of the form h(x, y) = p1(x)y + p2(x), where p1(x) and p2(x) are real coprime polynomials and p1(x) 6= 0, for a planar real algebraic quadratic system and we analyze the existence of this kind of invariant algebraic curves depending on the coefficients of the system. For some particular systems, we determine these invariant algebraic curves using orthogonal polynomials. The system given by Colin Christopher and Jaume Llibre as counterexample of Lins-Neto conjecture is one of the systems with an invariant algebraic curve of the form h(x, y) that can be expressed with orthogonal polynomials.