Formulas for Lyapunov exponents
  We derive a series summation formula for the average logarithm norm of the action of a matrix on the projective space. This formula is shown to be useful to evaluate some Lyapunov exponents of random $\SL$-matrix cocycles, which include a special class for which H. Furstenberg had provided an explicit integral formula. 
A. T. Baraviera, P. Duarte
math.DS