We consider fast oscillating random perturbations of dynamical systems in regions where one can introduce action-angle-type coordinates. In an appropriate time scale, the evolution of first integrals, under the assumption that the set of resonance tori is small enough, is approximated by a diffusion process. If action-angle coordinates can be introduced only piece-wise, the limiting diffusion process should be considered on an open-book space. Such a process can be described by differential operators, one in each page, supplemented by some gluing conditions at the binding of the open book.

中文翻译：

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多频系统中第一积分的噪声诱导演化的扩散近似

我们考虑动态系统的快速振荡随机扰动，该区域可以引入作用角类型的坐标。在适当的时间尺度上，在假设谐振圆托足够小的前提下，第一积分的演化通过扩散过程来近似。如果只能逐段地引入动作角坐标，则应在开放书本空间上考虑极限扩散过程。这种过程可以由差分运算符来描述，每页一页，在打开的书的装订处附加一些胶合条件。