A Two-Level Programming Approach to Volume Propagation in Higher-Dimensional Spaces

A set of algorithms designed for the analysis of phase-space perturbation propagation in dynamical systems is presented. The most important tasks are approximate volume estimation and determining the subset of the perturbation surface that is tangent to current lines. The algorithms are developed in a generic, dimension-independent fashion, but they can be partially evaluated with respect to the dimension of the space, yielding dimension specific, efficient algorithms. The MuPAD implementation of the algorithms and supporting libraries is also discussed