I will give several definitions of entropy at infinity for a dynamical system on a noncompact topological space. In the case of geodesic flows in negative curvature, in joint work with S. Gouëzel and S. Tapie, we showed that these definitions coincide. When the entropy at infinity is strictly smaller than the topological entropy, we obtained numerous interesting applications in the past few years. In a more recent work with A. Florio and A. Vaugon, we are able to prove that some of these properties still hold in the generality of hyperbolic flows on noncompact manifolds. I will try to give the flavour of these works.
Fanny Kassel
