精品文档---下载后可任意编辑非一致双曲集中的周期点的开题报告摘要：本文讨论非一致双曲集上周期点的存在性和稳定性。首先给出了非一致双曲集和周期点的定义，介绍了一些基本概念和定理。然后给出了单曲线和双曲线情况下周期点的存在性和稳定性的定理及证明。接着，本文引入了非一致双曲集的概念，并给出了直接和逆向非一致双曲集的定义和性质。针对非一致双曲集上的周期点，本文给出了周期点存在的充分条件和稳定性的定理及证明。并讨论了一些特别情况下的结果。最后，通过一些例子说明了结果的有效性。关键词：非一致双曲集，周期点，存在性，稳定性Abstract：In this paper, we study the existence and stability of periodic points on non-uniformly hyperbolic sets. Firstly, the definitions of non-uniformly hyperbolic sets and periodic points are given, and some basic concepts and theorems are introduced. Then, the existence and stability of periodic points are proved under the cases of single curve and hyperbolic curve.Next, the concept of non-uniformly hyperbolic sets is introduced, and the definitions and properties of direct and inverse non-uniformly hyperbolic sets are given. For the periodic points on non-uniformly hyperbolic sets, the sufficient conditions for the existence of periodic points and the stability theorem are given and proved. Some special cases are discussed as well. Finally, the effectiveness of the results is illustrated by some examples.Keywords: non-uniformly hyperbolic sets, periodic point, existence, stability
