LYAPUNOV EXPONENTS FOR Mob(D)-COCYCLES: A PROOF OF OSELEDETS THEOREM IN DIMENSION 2

Let T : M → M be an invertible measurable transformation, and μ be a T -invariant probability on M . Let π : E → M be a finite-dimensional real vector bundle over M , endowed with a measurable Riemannian metric ‖ · ‖. Let F : E → E be a measurable vector bundle automorphism over T : this means that π ◦ F = T ◦ π and the action Fx : Ex → ET (x) of F on each fiber Ex = π−1(x) is a linear isomorphism. We also call F a cocycle over T .