发表机构
TU Dresden（德累斯顿工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在 Banach 丛上建立广义 Hartman-Grobman 线性化定理，统一处理各类二分性，并推广到控制仿射系统。
AI 中文摘要
我们为局部紧度量空间上的抽象 Banach 丛上的斜积流提供了广义线性化定理，允许对一致与非一致、指数与强指数二分性进行统一处理。这是通过构造一个算子来实现的，该算子的不动点恰好是恒等映射的有界扰动的共轭，并给出了该算子是压缩映射的判据。在更强的假设下，我们改进论证以获得共轭的 Hölder 正则性。最后，我们将我们的结果应用于恢复非自治微分方程的已知结果，并获得流形上控制仿射系统的新的线性化结果。
英文摘要
We provide generalized linearization theorems for skew-product flows on abstract Banach bundles over locally compact metric spaces, allowing for a unified treatment of uniform and nonuniform, exponential and strong exponential dichotomies. This is accomplished by constructing an operator whose fixed points are exactly the conjugacies that are bounded perturbations of the identity, and by giving criteria under which this operator is a contraction. Under stronger assumptions we refine the argument to obtain Hölder regularity of the conjugacy. Finally, we apply our results to recover known results for non-autonomous differential equations and to obtain new linearization results for control-affine systems on manifolds.
