  Ergodicity of the systems with Nos\'e-Hoover thermostat are studied. The
dynamics of the heatbath variables are investigated and they can be periodic
when the system has quick oscillation. The periodic behaviour of them causes
the system to lose its ergodicity. The kinetic-moments method is also studied,
and the heatbath variables in this method are found to be chaotic. The chaotic
behaviour makes the whole system ergodic.
