  Two classes of time-periodic systems of ordinary differential equations with
a small nonnegative parameter, those with fast and slow time, are studied.
Right-hand sides of these systems are three times continuously differentiable
with respect to phase variables and the parameter, the corresponding
unperturbed systems are autonomous, conservative and have nine equilibrium
points. For the perturbed systems, which do not depend on the parameter
explicitly, we obtain the conditions yielding that the initial system has a
certain number of two-dimensional invariant surfaces homeomorphic to a torus
for each sufficiently small values of parameter and the formulas of such
surfaces. A class of systems with seven invariant surfaces enclosing different
configurations of equilibrium points is studied as an example of applications
of our method.
