Lorenz deterministic diffusion

The Lorenz 1963 dynamical system is known to reduce in the steady state to
a
one-dimensional motion of a classical particle subjected to viscous
damping in a past history-dependent potential field. If the potential
field is substituted by a periodic function of the position, the resulting
system shows a rich dynamics where (standard) diffusive behaviours,
ballistc
motions and trapping take place by varying the model control parameters.
This system permits to highlight the intimate relation between chaos and
long-time deterministic diffusion.