Anosov flows are example of chaotic dynamics, by this we usually mean
that the trajectories of two nearby points diverge exponentially fast,
hence a great sensitivity on initial conditions. Prime example of Anosov
flows are given by geodesic flows on negatively curved compact manifold.
I will explain how one can associate to an Anosov vector field X a
discrete spectrum (called de Pollicott-Ruelle resonances) and how the
eigenfunctions corresponding to the first resonance are related to
invariant measures describing the dynamics of the flow.