Martin Rasmussen:
An alternative approach to Sacker-Sell spectral theory
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.