动力系统中的诱导压

发布时间：2018-04-22 04:13

本文选题：动力系统 + 诱导拓扑压　；参考：《南京师范大学》2015年博士论文

【摘要】：本文定义紧致动力系统中的诱导拓扑压、诱导测度熵,研究它们的性质.具体的安排如下：在引言中,我们介绍动力系统中诱导拓扑压研究的背景.在第一章,我们介绍本文涉及到的遍历论和拓扑动力系统的预备知识.在第二章,我们定义紧致动力系统中的诱导拓扑压,研究诱导拓扑压与拓扑压的关系.在此基础上,得到诱导拓扑压的变分原理.作为诱导拓扑压的-个应用,指出BS维数是诱导拓扑压的特殊情形.我们还研究诱导拓扑压的平衡测度的存在性.在第三章,我们研究在因子映射下,诱导拓扑压之间的关系.具体地说,设π:(X,f)→(Y,g)为动力系统间的因子映射,也就是说π是从X到Y上与作用相容的连续满射,我们研究动力系统间诱导拓扑压的关系.作为一个应用,我们研究BS维数的零维扩张.在第四章,从拓扑的观念我们定义诱导测度熵,得到诱导测度熵的Katok熵公式.作为应用,我们得到：在符号空间,诱导测度熵是测度的Hausdorff维数.在第五章,我们定义可数符号空间上Markov转移映射的几乎可加势的诱导Gurevich压并且得到它的变分原理.
[Abstract]:In this paper, induced topological pressure and induced measure entropy in compact dynamical systems are defined and their properties are studied. The specific arrangements are as follows: in the introduction, we introduce the background of the study of induced topological pressure in dynamic systems. In the first chapter, we introduce the ergodic theory and the preliminary knowledge of topological dynamical system. In chapter 2, we define induced topological pressure in compact dynamical systems and study the relationship between induced topological pressure and topological pressure. On this basis, the variational principle of induced topological pressure is obtained. As an application of induced topological pressure, it is pointed out that BS dimension is a special case of induced topological pressure. We also study the existence of equilibrium measures of induced topological pressure. In chapter 3, we study the relationship between induced topological pressure under factor mapping. Specifically, let 蟺: XF) be a factor-mapping between dynamical systems, that is, 蟺 is a continuous surjection from X to Y which is compatible with action. We study the relation of induced topological pressure between dynamical systems. As an application, we study the zero dimensional extension of BS dimension. In chapter 4, we define the induced measure entropy from the concept of topology, and obtain the Katok entropy formula of the induced measure entropy. As an application, we obtain that the induced measure entropy is the Hausdorff dimension of the measure in the symbol space. In chapter 5, we define the induced Gurevich pressure of almost additive potential of Markov transition mapping on countable symbol space and obtain its variational principle.
【学位授予单位】：南京师范大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O19

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