Approximate a Discrete time dynamical system by a continuous one Is there any method by which we can somehow "embed" a non linear discrete time system into a continuous time dynamical system? (Assume discrete time system here is a set of non linear difference equations and a continuous time system is a set of differential equations) I know the reverse is quite easy but I cant seem to find methods by which I can approximate a discrete time system by a continuous one.

In Palis/de Melo's "Geometric theory of Dynamical Systems" there's a notion of "suspension of diffeomorphism": a way to construct vector field from a diffeomorphism of compact manifold $M$ embedding it as Poincare section for the flow. Not sure that it's exactly can be applied to your case, but nevertheless can give you an idea of solution.
