THE LYAPUNOV SPECTRUM OF FAMILIES OF TIME-VARYING MATRICES

For L(infinity)-families of time varying matrices centered at an unper turbed matrix, the Lyapunov spectrum contains the Floquet spectrum obt ained by considering periodically varying piecewise constant matrices. On the other hand, it is contained in the Morse spectrum of an associ ated flow on a vector bundle. A closer analysis of the Floquet spectru m based on geometric control theory in projective space and, in partic ular, on control sets, is performed. Introducing a real parameter rho greater than or equal to 0, which indicates the size of the L(infinity )-perturbation, we study when the Floquet spectrum, the Morse spectrum , and hence the Lyapunov spectrum all coincide. This holds, if an inne r pair condition is satisfied, for all up to at most countably many rh o-values.