Morse Decompositions for delay-differential equations

AbstractThe attractor for the scalar delay-differential equation x˙(t)=−f(x(t),x(t−1)) is shown to possess a Morse Decomposition, under the hypothesis of a negative feedback condition in the delay term. Using this decomposition, we prove results on the asymptotic rate of oscillation of solutions of the initial value problem. Existence of both slowly and rapidly oscillating periodic solutions is also proved