  Important information about the dynamical structure of a differential system
can be revealed by looking into its invariant compact manifolds, such as
equilibria, periodic orbits, and invariant tori. This knowledge is
significantly increased if asymptotic properties of the trajectories nearby
such invariant manifolds can be determined. In this paper, we present a result
providing sufficient conditions for the existence of invariant tori in
perturbative differential systems. The regularity, convergence, and stability
of such tori as well as the dynamics defined on them are also investigated. The
conditions are given in terms of their so-called higher order averaged
equations. This result is an extension to a wider class of differential systems
of theorems due to Krylov, Bogoliubov, Mitropolsky, and Hale.
