ABSTRACT
For a cocycle of invertible real n-by-n matrices, the multiplicative ergodic theorem gives an Oseledets subspace decomposition of ; that is, above each point in the base space, is written as a direct sum of equivariant subspaces, one for each Lyapunov exponent of the cocycle. It is natural to ask if these summands may be further decomposed into equivariant subspaces; that is, if the Oseledets subspaces are reducible. We prove a theorem yielding sufficient conditions for irreducibility of the trivial equivariant subspaces and for -valued cocycles and give explicit examples where the conditions are satisfied.
Disclosure statement
No potential conflict of interest was reported by the authors.