论文标题
具有第一个积分的系统的扰动：Reeb图上的运动
Perturbation of Systems with a First Integral: Motion on the Reeb Graph
论文作者
论文摘要
我们认为系统的长期行为靠近具有平稳第一积分的系统。在某些假设下，限制行为在某种程度上是通用的：它取决于第一个积分，确定性扰动和初始点。此外，对于一系列噪音，也是如此。特别是，从某种意义上说，确定性系统的长期行为可以是随机的，随机系统可以降低随机性。明确计算限制分布。
We consider the long-time behavior of systems close to a system with a smooth first integral. Under certain assumptions, the limiting behavior, to some extent, turns out to be universal: it is determined by the first integral, the deterministic perturbation, and the initial point. Furthermore, it is the same for a broad class of noises. In particular, the long-time behavior of a deterministic system can, in a sense, be stochastic and stochastic systems can have a reduced stochasticity. The limiting distribution is calculated explicitly.
