Homoclinic bifurcation with nonhyperbolic equilibria (Q876967)

The authors study the bifurcation of a homoclinic or heteroclinic orbit with a nonhyperbolic equilibrium, which is a pitchfork bifurcation point. The unperturbed system is assumed to possess a homoclinic orbit \(\Gamma\). Combining two discrete maps in the vicinity of \(\Gamma\), one of which describes the flow close to the equilibrium, while the other one models the dynamics far from equilibrium, it is shown that close to \(\Gamma\) homoclinic or periodic orbits exist.