Limit Behaviour of Independent Random Matrices' Products

The asymptotic behavior of the products of the independent identically distributed by $\mu$ unimodular random matrices is studied, when the conditions of the spectrum simplicity do not hold. In particular, the strong law of the large numbers is proved for the given dynamical system, and the conditions on the distribution $\mu$ are written, providing the difference of some fixed Lyapunov exponents. Moreover, we assume, that the distribution $\mu$ depends on some parameter a, and investigate the continuity of their limit characteristics from a for the random matrices' products.