Geodesic
Classification of Cocycles over Ergodic Automorphisms with Values in the Lorentz Group and Recurrence of Cocycles
Matematičeskie zametki, Tome 93 (2013) no. 6, pp. 869-877

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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.
Keywords: cocycle, ergodic automorphism, recurrence of cocycles, cohomology
Mots-clés : Lorentz group $\mathrm{SO}_0(1,d)$, conformal barycenter. 
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     author = {M. E. Lipatov},
     title = {Classification of {Cocycles} over {Ergodic} {Automorphisms} with {Values} in the {Lorentz} {Group} and {Recurrence} of {Cocycles}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {869--877},
     publisher = {mathdoc},
     volume = {93},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_6_a6/}
}
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M. E. Lipatov. Classification of Cocycles over Ergodic Automorphisms with Values in the Lorentz Group and Recurrence of Cocycles. Matematičeskie zametki, Tome 93 (2013) no. 6, pp. 869-877. http://geodesic.mathdoc.fr/item/MZM_2013_93_6_a6/