  Determining the existence of compact invariant manifolds is a central quest
in the qualitative theory of differential equations. Singularities, periodic
solutions, and invariant tori are examples of such invariant manifolds. A
classical and useful result from the averaging theory relates the existence of
isolated periodic solutions of non-autonomous periodic differential equations,
given in a specific standard form, with the existence of simple singularities
of the so-called guiding system, which is an autonomous differential equation
given in terms of the first non-vanishing higher order averaged function. In
this paper, we provide an analogous result for the existence of invariant tori.
Namely, we show that a non-autonomous periodic differential equation, given in
the standard form, has a normally hyperbolic invariant torus in the extended
phase space provided that the guiding system has a hyperbolic limit cycle. We
apply this result to show the existence of normally hyperbolic invariant tori
in a family of jerk differential equations.
