Lyapunov exponents,symmetric spaces,and a multiplicative ergodic theorem for semisimple Lie groups

The classical theory of Lyapunov characteristic exponents is reformulated in invariant geometric terms and carried over to arbitrary noncompact semisimple Lie groups with finite center. A multiplicative ergodic theorem (a generalization of a theorem of Oseledets) and the global law of large numbers are proved for semisimple Lie groups, as well as a criterion for Lyapunov regularity of linear systems of ordinary differential equations with subexponential growth of coefficients.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 30–46, 1987.