论文标题
迈向完全常规空间上动态系统的库普曼理论
Towards a Koopman theory for dynamical systems on completely regular spaces
论文作者
论文摘要
事实证明，紧凑型空间上的koopman线性化对紧凑型空间的拓扑系统或拓扑动力系统的线性化非常有用。在本文中，我们探讨了连续半流提供的动态，这是完全规则的空间，这些空间自然来自PDE的解决方案。我们在有限的连续函数的空间上为这些半流介绍了Koopman Semigroups。作为第一步，我们研究了它们的连续性及其无限发电机。然后，我们以理论（通过Kato的平等性）（通过派生）和晶格以代数来表征它们。最后，我们证明了吸引者的示例 - 这种Koopman方法可用于检查动态系统的属性。
The Koopman linearization of measure-preserving systems or topological dynamical systems on compact spaces has proven to be extremely useful. In this article we look at dynamics given by continuous semiflows on completely regular spaces which arise naturally from solutions of PDEs. We introduce Koopman semigroups for these semiflows on spaces of bounded continuous functions. As a first step we study their continuity properties as well as their infinitesimal generators. We then characterize them algebraically (via derivations) and lattice theoretically (via Kato's equality). Finally, we demonstrate-using the example of attractors-how this Koopman approach can be used to examine properties of dynamical systems.
