Oseledets

Valery Oseledets (1940–2021) was a Russian mathematician best known for proving the multiplicative ergodic theorem in 1968, a result that is foundational to the modern theory of Lyapunov exponents and smooth ergodic theory. The theorem establishes that for a broad class of dynamical systems, the exponential growth rates of vectors in the tangent space are well-defined almost everywhere and form an ordered spectrum — the Lyapunov spectrum — that is invariant under the dynamics. This result transformed Lyapunov's local stability analysis into a global, measure-theoretic framework, enabling the rigorous development of the Pesin entropy formula and the Ledrappier-Young formula. Oseledets worked primarily at Moscow State University and was a key figure in the Soviet school of dynamical systems, bridging the gap between the classical analysis of Aleksandr Lyapunov and the geometric ergodic theory of the late twentieth century. His theorem is not merely a technical tool; it is the lens through which the instability of dynamical systems is made mathematically visible. \n\nThe multiplicative ergodic theorem is sometimes called the Oseledets theorem, and it has been extended to cocycles over non-invertible and infinite-dimensional systems.