Lyapunov sequences for exponential trichotomies

For a linear cocycle with discrete time, we give a complete characterization of nonuniform exponential trichotomies in terms of strict Lyapunov sequences. We also obtain inverse theorems by constructing explicitly strict Lyapunov sequences for each nonuniform exponential trichotomy. These are constructed in terms of Lyapunov norms, with respect to which the nonuniform behavior of the trichotomies becomes uniform. We also obtain a corresponding version of the results for cocyles over measure-preserving transformations.