In this paper we prove that periodic boundary-value problems (BVPs) for delay
differential equations are locally equivalent to finite-dimensional algebraic
systems of equations. We rely only on regularity assumptions that follow those
of the review by Hartung et al. (2006). Thus, the equivalence result can be
applied to differential equations with state-dependent delays (SD-DDEs),
transferring many results of bifurcation theory for periodic orbits to this
class of systems. We demonstrate this by using the equivalence to give an
elementary proof of the Hopf bifurcation theorem for differential equations
with state-dependent delays. This is an alternative and extension to the
original Hopf bifurcation theorem for SD-DDEs by Eichmann (2006).Comment: minor revision, correcting mistakes in formulation of Lemma 2.3 and
A.5 (which are also present in the Journal paper): center of neighborhood
must be in C1, which is the case for the main theore
