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

The classical theory of dyapunov characteristic exponents is reformulated in invariant geometric terms and developed for arbitrary non-compact semi-simple Lie groups with finite centre. A multiplicative ergodic theorem and a global law of large numbers for semi-simple Lie groups, and criteria for the Lyapunov regularity of linear systems of ordinary differential equations with subexponential growth of coefficients are proved. Bibl. – 21.