Sébastien Neukirch Institut Jean le Rond d'Alembert Centre National de la Recherche Scientifique Université Pierre et Marie Curie Paris, France tel: +33 1 44 27 72 61 fax : +33 1 44 27 52 59 e-mail: sebastien.neukirch (-atat-) upmc.fr

Number of limit cycles of the Liénard equation

Hector Giacomini & Sébastien Neukirch

Physical Review E 56 \#4 (1997) 3809

Abstract : In this paper, we study a Li\'enard system of the form $\dot{x}=y-F(x) , \dot{y}=-x$, where $F(x)$ is an odd polynomial. 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 $R_n(x)$ whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.

PACS numbers : 05.45.+b , 02.30.Hq , 02.60.Lj , 03.20.+i

Key words : Liénard equation, limit cycles.