An adaptive method for the approximation of the generalized cell mapping

For the prediction of the long-term behavior and global analysis of nonlinear dynamical systems the generalized cell mapping is an efficient and powerful numerical tool. Since in general the generalized cell mapping cannot be computed directly it is necessary to develop a numerical method which allows us to approximate it. The purpose of our paper is to present such a method, where the approximation works in an adaptive way. Our method has the advantage that it can be controlled by a deterministic a priori error estimate. We illustrate its efficiency by an example.