  Observations and simulations of barred spiral galaxies have shown that, in
general, the spiral arms rotate at a different pattern speed to that of the
bar. The main conclusion from the bibliography is that the bar rotates faster
than the spiral arms with a double or even a triple value of angular velocity.
The theory that prevails in explaining the formation of the spiral arms in the
case of a barred spiral galaxy with two pattern speeds is the manifold theory,
where the orbits that support the spiral density wave are chaotic, and are
related to the manifolds emanating from the Lagrangian points L_1 and L_2 at
the end of the bar. In the present study, we consider an alternative scenario
in the case where the bar rotates fast enough in comparison with the spiral
arms and the bar potential can be considered as a perturbation of the spiral
potential. In this case, the stable elliptical orbits that support the spiral
density wave (in the case of grand design galaxies) are transformed into
quasiperiodic orbits (or 2D tori) with a certain thickness. The superposition
of these perturbed preccesing ellipses for all the energy levels of the
Hamiltonian creates a slightly perturbed symmetrical spiral density wave.
