Degenerated homoclinic bifurcations with higher dimensions (Q1567592)

The authors study periodic and homoclinic orbits produced from the degenerate homoclinic bifurcations, that is, they assume \[ \text{codim}(T_{r(t)} W^u+T_{r(t)} W^s)=2, \] where \(\Gamma= \{z=r(t): t\in\mathbb{R}, r(\pm\infty)=0\}\) is a homoclinic loop. They present results corresponding to the nonresonant and resonant cases and a method to establish a system of local coordinates near the homoclinic loop.