余伴随轨道上的噪声和耗散
Noise and dissipation on coadjoint orbits
摘要：
我们推导和研究随机耗散动力学coadjoint轨道上的噪声和耗散到机械系统所产生的对称性减少的理论，包括半直接产品的扩展。当李代数是半单的时，只要上李雅普诺夫指数是正的，就可以找到这类系统的随机吸引子。我们研究了两个典型的例子，自由刚体和重顶，其随机可积约化的发现和数值模拟的随机吸引子。
英文摘要：
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.
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