ArticleJournal of nonlinear science2018
Noise and Dissipation on Coadjoint Orbits.
Article in Journal of nonlinear science, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- Stochastic Variational Formulations of Fluid Wave-Current Interaction.Journal of nonlinear science · 2021Article
- Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation.Entropy (Basel, Switzerland) · 2020Article
- Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics.Entropy (Basel, Switzerland) · 2020Article
- Dynamics of non-holonomic systems with stochastic transport.Proceedings. Mathematical, physical, and engineering sciences · 2018Article
- Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows.Journal of nonlinear science · 2018Article
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3 authors.
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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 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.
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