The Gauss map has been shown to be a good example of a chaotic
discrete dynamical system, in that it exhibits in an accessible
fashion all the common features of such systems. The map is
simple enough that the relationship of numerical simulation of the map
to the exact map can be explored effectively.
We find that the numerical simulation of the map behaves significantly
differently, in that the numerical simulation is not chaotic, but is
still useful in that the Lyapunov exponent of the exact map can be
accurately calculated from the simulation.
We have in fact shown that this behaviour of numerical simulations is
We have also exhibited a new (though impractical) method for the calculation