Numerical analysis of high-dimensional
transfer operators
09-032 Thorsten Hüls.
Computing Sacker-Sell spectra in discrete time dynamical systems
In this paper we develop two 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 PP-P. If this residual is large,
then the difference equation has no exponential dichotomy. A second
criterion for detecting Sacker-Sell spectral intervals is the norm of
end points 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.
