精品文档---下载后可任意编辑Aubry 集的同宿轨的开题报告题目：Aubry 集的同宿轨摘要：Aubry 集是一类重要的几何对象，它是一种特别的闭合轨道。在介绍 Aubry 集的基本概念和性质的基础上，本文主要讨论 Aubry 集的同宿轨。我们首先给出同宿轨的定义和基本性质，然后探讨同宿轨的存在性和唯一性。接着，我们讨论同宿轨的拓扑结构和几何特征，并给出一些例子说明。最后，我们讨论同宿轨在动力系统和拓扑学中的应用。关键词：Aubry 集；同宿轨；动力系统；拓扑学Abstract:Aubry set is an important geometric object, which is a special closed orbit. Based on the introduction of the basic concepts and properties of Aubry set, this paper mainly studies the same homoclinic orbit of Aubry set. We first give the definition and basic properties of the same homoclinic orbit, and then explore the existence and uniqueness of the same homoclinic orbit. Next, we study the topological structure and geometric characteristics of the same homoclinic orbit, and give some examples to illustrate. Finally, we discuss the applications of the same homoclinic orbit in dynamical systems and topology.Keywords: Aubry set; same homoclinic orbit; dynamical system; topology
