COMPUTING SACKER-SELL SPECTRA IN DISCRETE TIME DYNAMICAL SYSTEMS.

In this paper we develop boundary value methods for detecting Sacker-Sell spectra in discrete time dynamical systems. The algorithms are advancements of earlier methods for computing projectors of exponential dichotomies. The first method is based on the projector residual P² - P. If this residual is large, then the difference equation has no exponential dichotomy. Further criterions for detecting Sacker-Sell spectral intervals are the norm of end points and midpoints of the solution of a specific boundary value problem. Refined error estimates for the underlying approximation process are given, and the resulting algorithms are applied to an example with known continuous Sacker-Sell spectrum, as well as to the variational equation along orbits of Hénon's map. [ABSTRACT FROM AUTHOR]