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Saddle connections and subharmonics are investigated for a class of forced second order differentiai equations which haVea fixed saddie point. In titese equations, which have linear damping and a nonlinear restoring term, tite ampiitude of the forcing terrn depends on displacemeni in tite system. Saddie connections are significant in nonlinear systems since their appearance signals a homociinic bifurca- tion. Tite approach uses a singular perturbation asetitod which has a fairiy broad appiication to saddle connections and also to Various subharmonics. The singular perturbation is unusual in that it uses a time-scaie which has to be constructed over an inflnite interVal. The system with a cubie restoring term and a quadratic amplitude is Iooked at in sorne detaii.

A singular perturbation method for saddle connections and subitarmonie of certain nonlinear differential equations with fixed saddle points