Baire classes of Lyapunov invariants

It is shown that no relations exist (apart from inherent ones) between Baire classes of Lyapunov transformation invariants in the compact-open and uniform topologies on the space of linear differential systems.
It is established that if a functional on the space of linear differential systems with the compact-open topology is the repeated limit of a multisequence of continuous functionals, then these can be chosen to be determined by the values of system coefficients on a finite interval of the half-line (one for each functional).
It is proved that the Lyapunov exponents cannot be represented as the limit of a sequence of (not necessarily continuous) functionals such that each of these depends only on the restriction of the system to a finite interval of the half-line.
Bibliography: 28 titles.