库普曼主义对动力系统中的吸引子有什么作用？
What can Koopmanism do for attractors in dynamical systems?
摘要：
利用相应的Koopman半群的渐近性质刻画了紧空间$K$上半流的长期行为.特别地，我们比较了不同的吸引子概念，如渐近稳定吸引子，Milnor吸引子和吸引中心。此外，我们给出了每一个上述性质的最小吸引子的特征。主要的方面是，我们只需要线性算子半群的技术和结果，因为Koopman半群允许一个可能的非线性半流的全局线性化。
英文摘要：
We characterize the longterm behavior of a semiflow on a compact space $K$ by asymptotic properties of the corresponding Koopman semigroup. In particular, we compare different concepts of attractors, such as asymptotically stable attractors, Milnor attractors and centers of attraction. Furthermore, we give a characterization for the minimal attractor for each mentioned property. The main aspect is that we only need techniques and results for linear operator semigroups, since the Koopman semigroup permits a global linearization for a possibly non-linear semiflow.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
