Exceptional sets for geodesic flows of noncompact manifolds

This talk is about so-called exceptional sets, that is, the set of points whose orbits do not accumulate at a given ``target set''. As a general (perhaps non-surprising) principle, the exceptional set is ``large'' if the target is ``small''.
After recalling some key results on this topic, I will discuss the case of the geodesic flow on a negatively curved Riemannian manifold.
We show that if the topological *-entropy of the target set is smaller than the topological entropy of the flow, then the exceptional set has full entropy. Some consequences are stated for targets which are invariant compact subsets and proper submanifolds.
This is joint work with Felipe Riquelme (PUC-Valparaíso).