Limit cycles of polynomial Liénard systems

Recently [H. Giacomini and S. Neukirch, Phys. Rev. E 56, 3809 (1997)], an algorithm to obtain the number of limit cycles of Liénard systems has been proposed. The quoted paper also includes a method to approximate the eventual limit cycles and a conjecture on the behavior of the algorithm. The algorithm is reviewed and some examples, which show that the algorithm is really efficient, are given. However, these examples indicate that the aforementioned conjecture may have been incorrectly stated. A different conjecture is proposed and some open questions are formulated. © 1998 The American Physical Society.