The asymptotic behaviour of cocycles over flows

Abstract

In 1968, V. I. Oseledets formulated the question of the convergence in Birkhoff’s theorem and in the multiplicative ergodic theorem for measurable cocycles over flows, under the condition of integrability at any fixed time. In 2016, A. M. Stepin and the author of this paper established convergence along subsets of density 1 on the time axis. Here we show that, moreover, convergence takes place modulo subsets of finite measure of the time axis.