Conditions for a diffeomorghism to be embedded in aC r flow

We will consider aC ^r diffeomorphism of the real lineR, and give a necessary and sufficient condition for aC ^r diffeomorphism ofR to be embedded (uniquely) in aC ^r flow. As an application, we do the same for diffeomorphisms of the circleS ¹ and a class of analytic diffeomorphisms of the planeR ².