Noise and dissipation on coadjoint orbits
Dynamical Systems
2017-08-02 v4 Mathematical Physics
math.MP
Chaotic Dynamics
Abstract
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect-product extension. Random attractors are found for this general class of systems when the Lie algebra is semi- simple, provided the top Lyapunov exponent is positive. We study two canonical examples, the free rigid body and the heavy top, whose stochastic integrable reductions are found and numerical simulations of their random attractors are shown.
Cite
@article{arxiv.1601.02249,
title = {Noise and dissipation on coadjoint orbits},
author = {Alexis Arnaudon and Alex L. Castro and Darryl D. Holm},
journal= {arXiv preprint arXiv:1601.02249},
year = {2017}
}