Numerische Spektralanalyse
unendlich-dimensionaler Transferoperatoren
07-039 Wolf-Jürgen Beyn, Alexander Lust.
A hybrid method for calculating Lyapunov exponents
In this paper we propose a numerical
method for computing all Lyapunov coefficients of a discrete time
dynamical system by spatial integration. The method extends an
approach of Aston and Dellnitz (1999) who use a box approximation of
an underlying ergodic measure and compute the first Lyapunov exponent
from a spatial average of the norms of the Jacobian for the iterated
map. In the hybrid method proposed here, we combine this approach with
classical QR-oriented methods by integrating R-factors with respect to
the invariant measure. In this way we obtain approximate values for
all Lyapunov exponents. Assuming somewhat stronger conditions than
those of Oseledec' multiplicative theorem, these values satisfy an
error expansion that allows to accelerate convergence through extrapolation.
