Zonotope Dynamics in Numerical Quality Control

Mathematical rigorous error bounds for the numerical approximation of dynamical systems have long been hindered by the wrapping effect. We present a new method which constructs high order zonotope (special polytopes) enclosures for the orbits of discrete dynamical systems. The wrapping effect can made arbitrarily small by controlling the order of the zonotopes. The method induces in the space of zonotopes a dynamical system of amazing geometrical complexity. We emphasis the visualization of the zonotopes to better understand the involved dynamics.