  This paper introduces a geometric method for proving ergodicity of degenerate
noise driven stochastic processes. The driving noise is assumed to be an
arbitrary Levy process with non-degenerate diffusion component (but that may be
applied to a single degree of freedom of the system). The geometric conditions
are the approximate controllability of the process the fact that there exists a
point in the phase space where the interior of the image of a point via a
secondarily randomized version of the driving noise is non void. The paper
applies the method to prove ergodicity of a sliding disk governed by
Langevin-type equations (a simple stochastic rigid body system). The paper
shows that a key feature of this Langevin process is that even though the
diffusion and drift matrices associated to the momentums are degenerate, the
system is still at uniform temperature.
