Modelling the inner parts of the Milky Way using invariant manifolds

In a series of papers we proposed a theory to explain the formation and properties of rings and spirals in barred galaxies. The building blocks of these structures are orbits trapped by the invariant manifolds of the periodic orbits around the unstable Lagrangian points located near the ends of the bar. Here, we will first present a comparison of the morphology of observed and theoretical spirals and rings. We will describe the mechanism used to obtain these features and then we will compare the morphology and kinematics of the rings and spirals obtained with the ones from observations. Finally, we will introduce the work done to model the spiral arms of the Milky Way using this new approach