混沌中Fokker-Planck算子的微扰理论
Perturbation theory for the Fokker-Planck operator in chaos
摘要：
一个完全混沌系统的平稳分布通常表现出分形结构，如果动力学方程稍微修改，它就会发生显着变化。在这种情况下，扰动技术预计不会起作用。相反，加性噪声的存在使平稳分布平滑，并且微扰理论变得适用。我们表明，一个扰动扩展的福克-普朗克演化算子产生令人惊讶的准确估计的长期平均值，否则不太可能的情况。
英文摘要：
The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this situation. In contrast, the presence of additive noise smooths out the stationary distribution, and perturbation theory becomes applicable. We show that a perturbation expansion for the Fokker-Planck evolution operator yields surprisingly accurate estimates of long-time averages in an otherwise unlikely scenario.
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