Noise and dissipation in rigid body motion
  Using the rigid body as an example, we illustrate some features of stochastic geometric mechanics. These features include: i) a geometric variational motivation for the noise structure involving Lie-Poisson brackets and momentum maps, ii) stochastic coadjoint motion with double bracket dissipation, iii) the Lie-Poisson Fokker-Planck description and its stationary solutions, iv) random dynamical systems, random attractors and SRB measures connected to statistical physics. 
Alexis Arnaudon, Alex L. De Castro, Darryl D. Holm
math.DS nlin.CD