Cocycles
The multiplicative ergodic theorem is stated in terms of matrix cocycles of a dynamical system. The theorem states conditions for the existence of the defining limits and describes the Lyapunov exponents. It does not address the rate of convergence.
A cocycle of an autonomous dynamical system is a map C : X×T → Rn×n satisfying
where X and T (with T = Z or T = R) are the phase space and the time range, respectively, of the dynamical system, and In is the n-dimensional unit matrix. The dimension n of the matrices C is not related to the phase space X.
Read more about this topic: Oseledets Theorem