关于连续动力系统中Banach正上密度回复点集的研究-应用数学专业论文.docxVIP

摘要 摘要 万方数据 万方数据 摘 要 本论文主要在连续动力系统中研究一种特别的回复性质，即 Banach 正上密 度回复性质. 类似于一般回复点集 R ?????的研究. 本论文对 Banach 正上密度回复 点集作了系统的研究. 全文共分为四章. 第一章主要对本论文的研究背景作了较为详细的介绍. 第二章主要介绍了本论文需要用到的一些基本概念和一些已知结论. 第三章研究了 Banach 正上密度回复点集的性质，给出了连续动力系统中一 个点是 Banach 正上密度回复点集的等价条件. 随后，讨论了 Banach 正上密度回 复点集与测度中心之间的关系. 第四章主要利用 Banach 正上密度回复点集的性质，研究一个连续动力系统 是 E ??系统的等价条件. 关键词：Banach 正上密度回复点集；测度中心；极小吸引中心；拟测度中 心；拟极小吸引中心； E ??系统；连续动力系统 II Abst Abstract ABSTRACT In this thesis, we mainly study an especial recurrent level in continuous dynamical systems, which is the properties of Banach positive upper density recurrent points. Similar to the properties of the set of recurrent points, in this thesis , we make a systematic study for the properties of Banach positive upper density recurrent points. This thesis is divided into four chapters. The first chapter gives a detailed description on the research background. The second chapter introduces some basic concepts and conclusions used in this thesis. In the third chapter, we study the properties of Banach positive upper density recurrent points, and give some equivalent conditions for a point in a continuous dynamical system to be a Banach positive upper density recurrent point. Subsequently, we discuss the relationship between Banach positive upper density recurrent points and measure center. In the fourth chapter, by using the properties of Banach positive upper density recurrent points, we present some equivalent conditions for a continuous dynamical system to be an E ??system. Keywords: Banach positive upper density recurrent point; measure center; the minimal center of attraction; quasi measure center; quasi minimal center of attraction; E ??system; continuous dynamical system III 目录 目录 Table of contents HYPERLINK \l _bookmark0 Chapter 1 Introduction 1 HYPERLINK \l _bookmark1 Chapter 2 Definitions and statements of main results 4 HYPERLINK \l _bookmark2 The introduction of continuous dynamical system 4 HYPERLINK \l _bookmark3 The introduction of Family