论文标题
多项式行为下非自主动力学的平滑线性化
Smooth linearization of nonautonomous dynamics under polynomial behaviour
论文作者
论文摘要
本文的主要目的是制定新的条件，以使非自主系统具有离散和连续时间的平滑线性化。我们的结果假设线性部分接受了不均匀的多项式二分法，并且相关的多项式二分法光谱表现出适当的光谱间隙和光谱带条件。这与文献中先前的大多数结果形成鲜明对比，后者假设线性部分接受指数二分法。我们的技术通过适当的时间修复时间来利用多项式和指数二分法之间的关系。
The main purpose of this paper is to formulate new conditions for smooth linearization of nonautonomous systems with discrete and continuous time. Our results assume that the linear part admits a nonuniform polynomial dichotomy and that the associated polynomial dichotomy spectrum exhibits appropriate spectral gap and spectral band conditions. This is in sharp contrast to most of the previous results in the literature which assumed that the linear part admits an exponential dichotomy. Our techniques exploit the relationship between polynomial and exponential dichotomies via a suitable reparametrization of time.
