Least Rattling Feedback from Strong Time-scale Separation

Many interesting dynamical systems in the world have a hierarchical structure. Here we explore how to leverage this structure to better understand and predict such systems. We assume that the dynamics on different scales can be viewed as independent, except for a clearly defined feedback loop: the slow motion defines the environment that fast dynamics live in, while fast motion maintains the rules governing effective slow dynamics. Focusing on this feedback loop, rather than the details of the fast or slow motion, may pave the way for generalizable insights about hierarchical systems. We illustrate on toy examples.