NUMBER OF LIMIT CYCLES OF THE LIENARD EQUATION

In this paper, we study a Lienard system of the form x ˙5y2F(x), y52x, where F(x) is an odd polyno- mial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials Rn(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system. @S1063-651X~97!02809-2#

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