因子映射的packing压和packing熵的条件变分原理
发布时间：2019-03-05 08:24
【摘要】：本文分为两部分,探讨动力系统中因子映射的packing压的半共轭公式和重分形分析中的packing熵的条件变分原理.第一部分定义次可加势函数族的packing拓扑压,上容量拓扑压,并给出次可加势函数族的packing压的两个半共轭公式.第二部分叙述了重分形分析中的基本知识并在弱specification性质下,证明了packing熵的条件变分原理.论文的大致框架如下：第一章,介绍了拓扑熵,拓扑压和重分形分析的背景.第二章,介绍了动力系统与遍历论理论中的一些基本概念及结果.第三章,定义了次可加势函数族的几种拓扑压,并给出次可加势函数族的packing压的半共轭公式.第四章,叙述了重分形中的一些定义和结论,并得到了packing熵的条件变分原理.
[Abstract]:This paper is divided into two parts. The semi-conjugate formula of packing pressure of factor mapping in dynamical system and the conditional variational principle of packing entropy in multifractal analysis are discussed. In the first part, we define the packing topological pressure and upper capacity topological pressure of the family of subadditive potential functions, and give two semi-conjugate formulas of the packing pressure of the family of subadditive potential functions. The second part describes the basic knowledge of multifractal analysis and proves the conditional variational principle of packing entropy under the weak specification property. The framework of this paper is as follows: in chapter 1, the background of topological entropy, topological pressure and multifractal analysis is introduced. In the second chapter, some basic concepts and results in the theory of dynamical system and ergodic theory are introduced. In chapter 3, some topological pressures of the family of subadditive potential functions are defined, and the semi-conjugate formulas of the packing pressure of the family of subadditive potential functions are given. In chapter 4, some definitions and conclusions of multifractal are described, and the conditional variational principle of packing entropy is obtained.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O19
本文编号：2434706
[Abstract]:This paper is divided into two parts. The semi-conjugate formula of packing pressure of factor mapping in dynamical system and the conditional variational principle of packing entropy in multifractal analysis are discussed. In the first part, we define the packing topological pressure and upper capacity topological pressure of the family of subadditive potential functions, and give two semi-conjugate formulas of the packing pressure of the family of subadditive potential functions. The second part describes the basic knowledge of multifractal analysis and proves the conditional variational principle of packing entropy under the weak specification property. The framework of this paper is as follows: in chapter 1, the background of topological entropy, topological pressure and multifractal analysis is introduced. In the second chapter, some basic concepts and results in the theory of dynamical system and ergodic theory are introduced. In chapter 3, some topological pressures of the family of subadditive potential functions are defined, and the semi-conjugate formulas of the packing pressure of the family of subadditive potential functions are given. In chapter 4, some definitions and conclusions of multifractal are described, and the conditional variational principle of packing entropy is obtained.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O19
【参考文献】
相关期刊论文 前1条
1 王小娟;;伪度量空间的紧致性分析[J];数学理论与应用;2012年02期
，本文编号：2434706
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