26 citations · 59 across the 24 of their papers we have counts for
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math-ph2016★ 26 cited
Momentum Maps and Stochastic Clebsch Action Principles
A. B. Cruzeiro, D. D. Holm, T. S. Ratiu
We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develo…
math-ph2015★ 5 cited
Stochastic variational principles for dissipative equations with advected quantities
Xin Chen, Ana Bela Cruzeiro, Tudor S. Ratiu
This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational principles yie…