Heteroclinic Orbits for Retarded Functional Differential Equations*

Suppose r is a heteroclinic orbit of a Ck functional differential equation i(t) =f(x,) with a-limit set a(T) and o-limit set w(T) being either hyperbolic equilibrium points or periodic orbits. Necessary and sufficient conditions are given for the existence of an 7 close to f in Ck with the property that i(t) = 3(x,) has a heteroclinic orbit p close to f. The orbits p are obtained from the zeros of a finite number of bifurcation functions G(b, 3) E iw”, BE lRd+ I. Transversality of f is characterized by the nondegeneracy of the derivative D,G. It is also shown that the f which have heteroclinic orbits near r are on a Ck submanifold of finite codimension = max{ 0, ind T} or on the closure of it, where ind r is the index of