COMMENT ON: LIENARD SYSTEMS, LIMIT CYCLES, AND MELNIKOV THEORY. AUTHOR'S REPLY

In papers by Sanjuan @Phys. Rev. E 57, 340 ~1998!# and Giacomini and Neukirch @Phys Rev. E 56, 3809 ~1997!# Lienard systems of the form ẋ5y2eF(x ,m), ẏ52x are studied. Sanjuan compares the results given by Melnikov theory with the results given by the Rn polynomials in the paper by Giacomini and Neukirch and conjectures that the roots of the Rn polynomials tend toward the roots of the Melnikov polynomial when n →` , for arbitrary values of e . We show here that this is true only when e→0 and that this fact strengthens the conjecture proposed by Giacomini and Neukirch. @S1063-651X~98!13112-4#