Heteroclinic orbits in singular systems: A unifying approach (Q1319928)

The author considers a singularly perturbed system \(\xi'= f(\xi,\eta,\varepsilon)\), \(\eta'=\varepsilon g(\xi,\eta,\varepsilon)\). It is assumed that \(\xi'= f(\xi,\alpha,0)\) has two manifolds of hyperbolic fixed points. The problem of the existence of heteroclinic orbits which join these manifolds is reduced to a bifurcation equation \(G(\alpha,\epsilon)= 0\).