Equivariant symplectic homology of Anosov contact structures
  We show that the differential in positive equivariant symplectic homology or linearized contact homology vanishes for non-degenerate Reeb flows with a continuous invariant Lagrangian subbundle (e.g. Anosov Reeb flows). Several applications are given, including obstructions to the existence of these flows and abundance of periodic orbits for contact forms representing an Anosov contact structure. 
Leonardo Macarini, Gabriel P. Paternain
math.SG math.DS