Geodesic
Recurrence of matrix cocycles
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2010), pp. 61-64 
M. E. Lipatov. Recurrence of matrix cocycles. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2010), pp. 61-64. http://geodesic.mathdoc.fr/item/VMUMM_2010_5_a11/
@article{VMUMM_2010_5_a11,
     author = {M. E. Lipatov},
     title = {Recurrence of matrix cocycles},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {61--64},
     year = {2010},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_5_a11/}
}
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This paper considers measurable cocycles with values in the subgroup of $SL(2,\mathbb C)$ of diagonal and skew-diagonal matrices over an ergodic, transformation preserving the probability measure. We prove the recurrence of such cocycles under certain conditions as well as the equivalence of two definitions of recurrence.