Numerical approximation and spectral analysis of infinite-dimensional dynamical systems
03-059 Wolf-Jürgen Beyn, Thorsten Hüls.
Error estimates for approximating non-hyperbolic
heteroclinic orbits of maps
In this paper we consider heteroclinic orbits in discrete time dynamical systems
that connect a hyperbolic fixed point to a non-hyperbolic fixed point with a
one-dimensional center direction. A numerical method for approximating the
heteroclinic orbit by a finite orbit sequence is introduced and a detailed error
analysis is presented. The loss of hyperbolicity requires special tools for proving
the error estimate - the polynomial dichotomy of linear difference equations and a
(partial) normal form transformation near the non-hyperbolic fixed point.
This situation appears, for example, when one fixed point undergoes a flip bifurcation.
For this case, the approximation method and the validity of the error estimate
is illustrated by an example.
