Abstract
Li\'enard systems constitute a general class of two-dimensional autonomous systems, among which the van der Pol equation is found. Recently Giacomini and Neukirch [Phys. Rev. E 57, 3809 (1997)] introduced a sequence of polynomials whose roots are related to the number and location of limit cycles of Li\'enard systems. We show that in the limit of these sequences, the same information is given by a polynomial which Melnikov theory associates with a given Li\'enard system, and discuss the relationship existing among them.
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