  Utilizing concepts from dynamical systems theory, we demonstrate how the
existence of light rings, or fixed points, in a spacetime will give rise to
families of periodic orbits and invariant manifolds in phase space. It is shown
that these structures define the shape of the black hole shadow as well as a
number of salient features of the spacetime lensing. We illustrate this through
the analysis of lensing by a hairy black hole.
