Special features of galactic dynamics: Disc dynamics

This is a tutorial presentation of special features of galactic disc dynamics, which completes our introduction to galactic dynamics initially presented in [30]. The emphasis is on topics where galactic dynamics and celestial mechanics share common starting points and/or methods of approach. We start by giving some definitions and general notions on the link between observations and dynamical modeling of discs. Then we focus on the application of resonant Hamiltonian perturbation theory in disc resonances. By examining in detail the case of the Inner Lindblad resonance, we demonstrate how resonant perturbation theory leads to an orbital theory of spiral structure in normal galaxies. Passing to barred galaxies, the phase space structure and the role of chaos in the corotation region are analyzed. This is accomplished by a summary of the modern theory of invariant manifolds of unstable periodic orbits in the vicinity of L₁ or L₂, which can interpret the generation of spiral patterns by chaotic orbits beyond corotation. Some additional topics, potentially important for disc dynamics, are briefly commented.