Lyapunov Exponents for Random Perturbations of Coupled Standard Maps

In this paper, we give a quantitative estimate for the first N Lyapunov exponents for random perturbations of a natural class of 2 N -dimensional volume-preserving systems exhibiting strong hyperbolicity on a large but noninvariant subset of the phase space. Concrete models covered by our setting include systems of coupled standard maps, in both ‘weak’ and ‘strong’ coupling regimes.