Rigorously computed orbits of dynamical systems without the wrapping effect

A new method for rigorously computing orbits of discrete dynamical systems is introduced. High order zonotope enclosures of the orbit are computed, using only matrix algebra. The wrapping effect can be made arbitrarily small by choosing the order high enough. The method is easy to implement and especially suited for parallel computing. It is compared to other well known strategies, and several examples are given.