Numerical Orbits of Chaotic Processes Represent True Orbits

It is the nature of chaotic processes of the form x n+ i = f(xn ), where f : Rd —• Rd , that different orbits starting close together will move apart rapidly.  When following an orbit numerically, a common accuracy is about 14 digits. For chaotic systems such as the logistic map (or in twodimensions, the Hénon map), distances between two nearby orbits on average grow geometrically on every iterate.