Global Bifurcations Caused by the Unfolding of a Homoclinic Orbit

摘要

A class of smooth vector fields on R the set of real numbers cubed, consisting ofvector fields with a hyperbolic singularity of a kind described and a homoclinic orbit, that is, an orbit converging to the singularity both for positive and negative times, is considered. Center manifolds, generalized homoclinic orbits, and multivalued maps are all discussed, and the bifurcation theorems are presented.