We study the bar-driven dynamics in the inner part of the Milky Way by using invariant manifolds. This theory has been successfully applied to describe the morphology and kinematics of rings and spirals in external galaxies, and now, for the first time, we apply it to the Milky Way. We compute the orbits confined by the invariant manifolds of the unstable periodic orbits located at the ends of the bar. We discuss whether the COBE/DIRBE bar and the Long bar compose a single bar or two independent bars and perform a number of comparisons which, taken together, argue strongly in favour of the former. More specifically, we favour the possibility that the so-called COBE/DIRBE bar is the boxy/peanut bulge of a bar whose outer thin parts are the so-called Long bar. This possibility is in good agreement both with observations of external galaxies, with orbital structure theory and with simulations. We then analyse in detail the morphology and kinematics given by five representative Galactic potentials. Two have a Ferrers bar, two have a quadrupole bar and the last one a composite bar. We first consider only the COBE/DIRBE bar and then extend it to include the effect of the Long bar. We find that the large-scale structure given by the manifolds describes an inner ring, whose size is similar to the near and far 3-kpc arm, and an outer ring, whose properties resemble those of the Galactic Molecular Ring. We also analyse the kinematics of these two structures, under the different galactic potentials, and find they reproduce the main over-densities found in the galactic longitude-velocity CO diagram. Finally, we consider for what model parameters, the global morphology of the manifolds may reproduce the two outer spiral arms. We conclude that this would necessitate either more massive and more rapidly rotating bars, or including in the potential an extra component describing the spiral arms.
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