Journal of Statistical Physics, Vol. 112, Nos. 1/2, July 2003. p. 193-218.
I show how continuous products of random transformations constrained by a generic group structure can be studied by using Iwasawa’s decomposition into ‘‘angular,’’ ‘‘diagonal,’’ and ‘‘shear’’ degrees of freedom. In the case of a Gaussian process a set of variables, adapted to the Iwasawa decomposition and still having a Gaussian distribution, is introduced and used to compute the statistics of the finite-time Lyapunov spectrum of the process. The variables also allow to show the exponential freezing of the ‘‘shear’’ degrees of freedom, which contain information about the Lyapunov eigenvectors.