  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.
