Abstract:

In the classical Sacker-Sell spectral theory, growth rates of linear nonautonomous dynamical systems are characterized by means of exponential dichotomies. The Sacker-Sell spectrum is given by the union of finitely many closed intervals, each of which is associated to a spectral manifold. This yields a linear decomposition of the extended phase space. In this talk, we propose an alternative way to obtain the Sacker-Sell spectrum: In contrast to the classical approach, we start with a linear decomposition, which is given by the finest Morse decomposition in the projective space. Then the growth rates attained in the components of this Morse decomposition yield the Sacker-Sell spectrum.