The Multiplicative Ergodic Theorem

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A volume-based approach to the multiplicative ergodic theorem on Banach spaces (2015, background): “, [1, 2, 3, 4]; for additional treatments, see Section 3.”
Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system (2015, methodology): “[84]) characterize the rates of exponential growth of the singular values of fundamental matrix of the linearized system.”
A concise proof of the Multiplicative Ergodic Theorem on Banach spaces (2014, methodology): “Corollary 15 (The Oseledets splitting).”
Isomorphic extensions and applications (2015, unknown): “Oseledec’s theorem [20], he proves the following:”
Generalized Nonuniform Dichotomies and Local Stable Manifolds (2010, methodology): “Then, in [14] Ruelle gave a proof of this theorem based on the study of perturbations of products of matrices occurring in Oseledets’ multiplicative ergodic theorem [8].”
Euler's constant: Euler's work and modern developments (2013, background): “A corollary of the multiplicative ergodic theorem proved by Oseledec in 1968 (see [241], [252]) asserts that with probability one all these logarithmic exponents take constant values, provided the probability distribution on random matrices satisfies (3.”