Classification of Cocycles over Ergodic Automorphisms with Values in the Lorentz Group and Recurrence of Cocycles

It is proved that any $\mathrm{SO}_0(1,d)$-valued cocycle over an ergodic (probability) measure-preserving automorphism is cohomologous to a cocycle having one of three special forms; the recurrence property of such cocycles is also studied.