Topological horseshoes and delay differential equations

We show that if an ordinary differential equation x' = f (x), where x is an element of R-n and f is an element of C-1, has a topological horseshoe, then the corresponding delay equation x'(t) = f(x(t - h)) for small h > 0 also has a topological horseshoe, i.e. symbolic dynamics and an infinite number of periodic orbits. A method of computation of h is given in terms of topological properties of solutions of differential inclusion x'(t) is an element of f(x(t)) + B(0, delta).