Existence of dichotomies and invariant splittings for linear differential systems IV

The structure of linear skew-product dynamical systems is investigated in the case in which bounded orbits are admitted. The spectral decomposition theorem is applied and estimates are obtained giving lower bounds on the number of independent bounded solutions of a time varying linear ordinary differential system based on the limiting behavior of the system. The results are also used to study the stability behavior of a class of linear difference systems.