Consider the system x = y (a1x + a3x3 + +a2n+1x2n+1), y =

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Consider the system

˙ x = y − (a1x + a3x3 +· · ·+a2n+1x2n+1), ˙ y = −x.

Prove by induction that at most n small-amplitude limit cycles can be bifurcated form the origin.

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