Lyapunov exponents and other spectra for differential algebraic equations

Abstract:
To characterize the asymptotic behavior and the growth rate of solutions of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs), basic spectral notions such as Lyapunov- and Bohl exponents, as well as Sacker-Sell spectra are discussed. For DAEs in strangeness-free form, the results extend those for ordinary differential equations, but only under additional conditions. This has consequences concerning the boundedness of solutions of inhomogeneous equations. Also, linear subspaces of leading directions are characterized, which are associated with spectral intervals and which generalize eigenvectors and invariant subspaces as they are used in the linear time-invariant setting.