Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle connections and also to various subharmonics. The singular perturbation is unusual in that it uses a time-scale which has to be constructed over an infinite interval. The system with a cubic restoring term and a quadratic amplitude is looked at in some detail.
@article{urn:eudml:doc:43727,
title = {A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {3},
year = {1990},
pages = {89-107},
zbl = {0711.34073},
mrnumber = {MR1060281},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43727}
}
Smith, Peter. A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.. Revista Matemática de la Universidad Complutense de Madrid, Tome 3 (1990) pp. 89-107. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43727/