Inertial and slow manifolds for delay equations with small delays

Yu.A. Ryabov and R.D. Driver proved that delay equations with small delays have Lipschitz inertial manifolds. We prove that these manifolds are smooth. In addition, we show that expansion in the small delay can be used to obtain the dynamical system on the inertial manifold. This justifies “post-Newtonian” approximation for delay equations.