  In this paper we consider a manifold with a dynamical vector field and
inquire about the possible tangent bundle structures which would turn the
starting vector field into a second order one. The analysis is restricted to
manifolds which are diffeomorphic with affine spaces. In particular, we
consider the problem in connection with conformal vector fields of second order
and apply the procedure to vector fields conformally related with the harmonic
oscillator (f-oscillators) . We select one which covers the vector field
describing the Kepler problem.
