On the simplicity of the Lyapunovspectrum of products of randommatricesLudwig

@inproceedings{Arnold1995OnTS,
title={On the simplicity of the Lyapunovspectrum of products of randommatricesLudwig},
author={Arnold and N. D. Cong},
year={1995}
}

Assuming that the underlying probability space is non-atomic we prove that products of random matrices (linear cocycles) with simple Lyapunov spectrum form an L p-dense set (1 p < 1) in the space of all cocy-cles satisfying the integrability conditions of the multiplicative ergodic theorem. However, the linear cocycles with one-point spectrum are also L p-dense. Further, in any L 1-neighborhood of an orthogonal cocycle there is a diagonalizable cocycle. For products of independent identicallyâ€¦Â CONTINUE READING