  Analyticity and other properties of the largest or smallest Lyapunov exponent
of a product of real matrices with a "cone property" are studied as functions
of the matrices entries, as long as they vary without destroying the cone
property. The result is applied to stability directions, Lyapunov coefficients
and Lyapunov exponents of a class of products of random matrices and of
dynamical systems. The method is based on the classical theory of the Mayer
series in Statistical Mechanics of rarefied gases.
