  We construct new substantive examples of non-autonomous vector fields on
3-dimensional sphere having a simple dynamics but non-trivial topology. The
construction is based on two ideas: the theory of diffeomorpisms with wild
separatrix embedding (Pixton, Bonatti-Grines, etc.) and the construction of a
non-autonomous suspension over a diffeomorpism (Lerman-Vainshtein). As a
result, we get periodic, almost periodic or even nonrecurrent vector fields
which have a finite number of special integral curves possessing exponential
dichotomy on $\R$ such that among them there is one saddle integral curve (with
an exponential dichotomy of the type (3,2)) having wildly embedded
two-dimensional unstable separatrix and wildly embedded three-dimensional
stable manifold. All other integral curves tend, as $t\to \pm \infty,$ to these
special integral curves. Also we construct another vector fields having $k\ge
2$ special saddle integral curves with tamely embedded two-dimensional unstable
separatrices forming mildly wild frames in the sense of Debrunner-Fox. In the
case of periodic vector fields, corresponding specific integral curves are
periodic with the period of the vector field, and they are almost periodic for
the case of almost periodic vector fields.
