Stability and Collapse of Lyapunov Spectrum

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Lyapunov exponents and Oseledets spaces are a rough analogue of eigenvalues and eigenspaces for stationary products of matrices (or operators). We are interested in the stability or otherwise of these exponents and spaces when the family of matrices or operators is perturbed in a stationary way. We study a family of linear operators coming from a random dynamical system consisting of a stationary composition of Blaschke products.