Numerical Analysis of equivariant evolution equations
10-096 Wolf-Jürgen Beyn, Alexander Lust.
Error analysis of a hybrid method for
computing Lyapunov exponents
In a previous paper [6] we suggested a
numerical method for computing all Lyapunov exponents of a
dynamical system by spatial integration with respect to an
ergodic measure. The method extended an earlier approach of
Aston and Dellnitz [2] for the largest Lyapunov exponent by
integrating the diagonal entries from the QR-decomposition
of the Jacobian for an iterated map. In this paper we provide
an asymptotic error analysis of the method for the case in
which all Lyapunov exponents are simple. We employ Oseledec
multiplicative ergodic theorem and impose certain hyperbolicity
conditions on the invariant subspaces that belong to
neighboring exponents. The resulting error expansion shows that
one step of extrapolation is enough to obtain exponential decay
of errors.
