  A simple deterministic and time reversal invariant type of thermostat is
proposed to be used for computer simulations of classical systems. It acts on
collisions with the walls of the container exclusively. It maps the incoming
and outgoing velocity of an impinging particle onto each other uniquely, in a
way that satisfies a detailed balance condition with respect to the (local)
wall temperature. It is fast to implement on a computer, leads to rapid
equilibration or approach to a stationary nonequilibrium state and it effects
the physical properties of the system in a narrow boundary layer only. Because
of the deterministic nature it is especially suitable for studying dynamical
systems characteristics, such as Lyapunov exponents and fractal dimensions of
attractors. A few successful applications have been reported already.
