Real cone contractions and analyticity properties of the characteristic exponents

In this paper, we use the Hilbert projective metric and Birkhoff’s theorem to
prove a generalization of a result of Ruelle. We consider a random product of
operators preserving a family of proper closed convex cones. We show that,
without any topological assumption, the characteristic exponent depends real
analytically on the data of the problem. As an example, we apply this result to
cocycles in Sinai billiards: the characteristic exponent behaves real analytically
under small perturbations of the cocycle in an appropriate Banach space.