Resumen de On the algebraic limit cycles of quadratic systems

Javier Chavarriga Soriano , Jaume Llibre , Jordi Sorolla Bardají

• Four type of algebraic limit cycles for quadratic systems are known: one of degree two and three of degree four. But there is not a definitive result about the algebraic limit cycles of a quadratic system. In this paper we give a characterization of the irreducible invariant algebraic curves of fourth degree of a quadratic system containing an oval which is an algebraic limit cycle of the system, showing that there are exactly four families of algebraic limit cycles of degree 4 for quadratic systems.