Bifurcation from degenerate homoclinics in periodically forced systems (original) (raw)

This work investigates the bifurcation phenomena arising from degenerate homoclinic solutions in periodically forced systems described by ordinary differential equations. The analysis focuses on the conditions under which homoclinic solutions exist and how changes in parameters influence these solutions. A series of theorems are presented, detailing the necessary conditions and implications of these bifurcations, particularly emphasizing situations with varying numbers of parameters. The implications for future research involve understanding more complex structures in the presence of different forces and their effects on stability.