  The classical theorems about singular perturbation reduction (due to Tikhonov
and Fenichel) are concerned with convergence on a compact time interval (in
slow time) as a small parameter approaches zero. For unbounded time intervals
Hoppensteadt gave a convergence theorem, but his criteria are generally not
easy to apply to concrete given systems. We state and prove a convergence
result for autonomous systems on unbounded time intervals which relies on
criteria that are relatively easy to verify, in particular for the case of a
one-dimensional slow manifold. As for applications, we discuss several reaction
equations from biochemistry.
