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Journal of Nonlinear Science

pp 1–55

First Online: 17 July 2017Received: 11 June 2017Accepted: 12 June 2017


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 in details 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.

KeywordsStochastic geometric mechanics Euler-Poincaré theory Coadjoint orbits Invariant measures Random attractors Lyapunov exponents Communicated by Paul Newton.

Mathematics Subject Classification37H10 37J15 60H10  Download fulltext PDF

Autor: Alexis Arnaudon - Alex L. De Castro - Darryl D. Holm


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