Limit behavior of independent random matrices' products (Q1598920)

The asymptotic behavior of the products of independent identically distributed unimodular random matrices according to \(\mu\) is studied in the case when the conditions for the simplicity of the spectrum do not hold. In particular, the strong law of large numbers is proven for a given dynamical system, and conditions on the distribution \(\mu \) are established, which ensure that some fixed Lyapunov exponents are different. Moreover, the author assumes that the distribution \(\mu\) depends on some parameter \(a\) and investigates the continuity of the limit characteristics in \(a\) for products of random matrices.