Contact Anosov flows on hyperbolic 3–manifolds

Geodesic flows of Riemannian or Finsler manifolds have been the only known contact Anosov flows. We show that even in dimension 3 the world of contact Anosov flows is vastly larger via a surgery construction near an E -transverse Legendrian link that encompasses both the Handel-Thurston and Goodman surgeries and that produces flows not topologically orbit equivalent to any algebraic flow. This includes examples on many hyperbolic 3-manifolds, any of which have remarkable dynamical and geometric properties.