Noise and dissipation in rigid body motion

2016/06/20 by Arnaudon, Alexis, De Castro, Alex L., Holm, Darryl D. · 1 citation
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.1606.06308

Abstract

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.

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• Random attractor and SRB measure for stochastic Hopf bifurcation under discretization

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