On the Perron exponents of discrete linear systems

This note studies properties of Perron or lower Lyapunov exponents for discrete time varying system. It is shown that for diagonal system of order s there are at most 2^s-1 lower Lyapunov exponents. By example it is demonstrated that in non-diagonal case it is possible to have arbitrarily many different Perron exponents. Finally it is shown that the exponent is almost everywhere equal to the lower Lyapunov exponent of the matrices coefficient sequence.