Generic periodic solutions of functional differential equations

AbstractConsider the class of retarded functional differential equations x(t) = f(xt), (∗) where xt(θ) = x(t + θ), −1 ⩽ θ ⩽ 0, so xt ϵ C = C([−1, 0], Rn), and f∈=Cr(C,Rn). Let 2 ⩽ r ⩽ ∞ and give X the appropriate (Whitney) topology. Then the set of f∈ such that all fixed points and all periodic solutions of (∗) are hyperbolic is residual in