论文标题
超线性化的可见和隐藏的可观察物
Visible and hidden observables in super-linearization
论文作者
论文摘要
如果将有限维嵌入为线性系统（称为有限维的koopman嵌入），我们将其称为“超线化”系统。否则说，如果可以通过添加有限的可观察到的动态来线性化。我们介绍了此类嵌入的可见和隐藏可观察物的概念，这些嵌入方式大致是明确出现在原始系统中的观测值，而这些观察力是嵌入的，但对于嵌入而言是必需的。不同的嵌入可以具有不同数量的隐藏和可见的可观察物。在本文中，我们在其所有超线性结局中为系统的可见光数量得出了一个紧密的下限。
We call a system super-linearizable if it admits finite-dimensional embedding as a linear system -- known as a finite-dimensional Koopman embedding; said otherwise, if its dynamics can be linearized by adding a finite set of observables. We introduce the notions of visible and hidden observables for such embeddings which, roughly speaking, are the observables that explicitly appear in the original system and the ones that do not, but yet are necessary for its embedding. Distinct embeddings can have different numbers of hidden and visible observables. In this paper, we derive a tight lower bound for the number of visible observables of a system among all its super-linearizations.
