Visible and hidden observables in super-linearization
Visible and hidden observables in super-linearization
复制标题
超线性化中的可见和隐藏的可观测量
DOI：
--
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
M. Belabbas
中科院分区：
文献类型：
--
作者：
M. Belabbas
我们称一个系统为超线性的，如果它允许有限维嵌入作为一个线性系统——称为有限维库普曼嵌入；换句话说，如果它的动力学可以线性化，通过添加一组有限的可观测值。我们为这样的嵌入引入了可见和隐藏可观察对象的概念，粗略地说，这些可观察对象是显式出现在原始系统中的可观察对象和不显式出现在原始系统中的可观察对象，但它们对于嵌入是必要的。不同的嵌入可以有不同数量的隐藏和可见的可观察对象。本文导出了一个系统在其所有超线性化中可见观测数的紧下界。
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 num-bers 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.