ABSTRACT
Galaxies have traditionally been viewed as integrable or nearly integrable systems, in which the majority of stellar orbits are regular, respecting as many integrals of motion as there are degrees of freedom. Most regular orbits in non-integrable potentials can be associated with a definite resonance and have a shape that reflects the order of the resonance. This chapter focuses on torus construction, resonances and their effect on the structure of orbits, the orbital content of triaxial potentials with central point masses, mixing, and the relation between chaos in the gravitational TV-body problem and chaos in smooth potentials. Stochastic motion introduces a new time scale into galactic dynamics, the mixing time. Mixing is the process by which a non-uniform distribution of particles in phase space relaxes to a uniform distribution, at least in a coarse-grained sense. Non-integrable potentials often exhibit a transition to global stochasticity as the magnitude of some perturbation parameter is increased.
