Consider the Linard system given by x = y (a1x + a2x2 + a3x3),

Consider the Liénard system given by

˙ x = y − ǫ(a1x + a2x2 + a3x3), ˙ y = −x.

Prove that for sufficiently small ǫ, there is at most one limit cycle that is asymptotic to a circle of radius r =

4|a1|

3|a3|

.