Numerische Spektralanalyse
unendlich-dimensionaler Transferoperatoren
08-081 Thorsten Hüls.
Numerical computation of dichotomy rates and projectors in discrete time
We introduce a characterization of
exponential dichotomies for linear difference equations that can be
tested numerically and enables the approximation of dichotomy rates
and projectors with high accuracy. The test is based on computing the
bounded solutions of a specific inhomogeneous difference equation. For
this task a boundary value and a least squares approach is
applied. The results are illustrated using Henon's map. We
compute approximations of dichotomy rates and projectors of the
variational equation, along a homoclinic orbit and an orbit on the
attractor. For both approaches, we analyze in detail errors that
occur, when restricting the infinite dimensional problem to a finite
interval.
