On the Lagrange and Markov Dynamical Spectra for Anosov Flows in   dimension 3
  We consider the Lagrange and the Markov dynamical spectra associated with a conservative Anosov flow on a compact manifold of dimension $3$ (including geodesic flows of negative curvature and suspension flows). We show that for a large set of real functions and typical conservative Anosov flows, both the Lagrange and Markov dynamical spectra have a non-empty interior. 
Sergio Augusto Roma\~na Ibarra
math.DS