This is quite a difficult question. Consider the Linard system (10.10) x = y F(x),

This is quite a difficult question. Consider the Liénard system

(10.10) ˙ x = y − F(x), ˙ y = −x, where F(x) = (a1x + a3x3 + a5x5) is odd. Prove that system (10.10) has at most two limit cycles.