The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects

In this paper we consider the singular value decomposition (SVD) of a fundamental matrix solution in order to approximate the Lyapunov and exponential dichotomy spectra of a given system. One of our main results is to prove that SVD techniques are sound approaches for systems with stable and distinct Lyapunov exponents. We also show how the information which emerges with the SVD techniques can be used to obtain information on the growth directions associated to given spectral intervals.