On random perturbations of Hamiltonian systems with many degrees of freedom
On random perturbations of Hamiltonian systems with many degrees of freedom
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DOI：
10.1016/s0304-4149(01)00083-7
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发表时间：
2001-08
影响因子：
1.4
通讯作者：
M. Freidlin;Matthias Weber
中科院分区：
文献类型：
--
作者：
M. Freidlin;Matthias Weber
考虑一类多自由度Hamilton系统的随机扰动。我们假设扰动由两个分量组成：一个较大的，保持能量和破坏所有其他的第一积分，和一个较小的，这是一个非退化的白色噪声型过程。在这些假设下，我们证明了这样一个扰动系统的长时间行为描述的扩散过程对应的系统的哈密顿量的图。该图是同胚的哈密尔顿的水平集的所有连通分支的集合。我们计算的微分算子支配的过程中的边缘的图和胶合条件的顶点。
We consider a class of random perturbations of Hamiltonian systems with many degrees of freedom. We assume that the perturbations consist of two components: a larger one which preserves the energy and destroys all other first integrals, and a smaller one which is a non-degenerate white noise type process. Under these assumptions, we show that the long time behavior of such a perturbed system is described by a diffusion process on a graph corresponding to the Hamiltonian of the system. The graph is homeomorphic to the set of all connected components of the level sets of the Hamiltonian. We calculate the differential operators which govern the process inside the edges of the graph and the gluing conditions at the vertices.