Exceptional sets for geodesic flows of noncompact manifolds

Abstract

For a geodesic flow on a negatively curved Riemannian manifold M and some subset A ⊂ T 1 M , we study the limit A-exceptional set, that is, the set of points whose ω-limit does not intersect A. We show that if the topological * -entropy of A is smaller than the topological entropy of the geodesic flow, then the limit A-exceptional set has full topological entropy. This result follows as a consequence of the construction of basic sets, with arbitrarily large entropy, over which the dynamics is conjugated to a suspension flow over a subshift of finite type. As an application, we compute the entropy of limit exceptional sets of invariant compact subsets and proper submanifolds.