發(fā)布時間：2018-04-22 04:13

  本文選題：動力系統(tǒng) + 誘導拓撲壓　； 參考：《南京師范大學》2015年博士論文

【摘要】：本文定義緊致動力系統(tǒng)中的誘導拓撲壓、誘導測度熵,研究它們的性質(zhì).具體的安排如下：在引言中,我們介紹動力系統(tǒng)中誘導拓撲壓研究的背景.在第一章,我們介紹本文涉及到的遍歷論和拓撲動力系統(tǒng)的預(yù)備知識.在第二章,我們定義緊致動力系統(tǒng)中的誘導拓撲壓,研究誘導拓撲壓與拓撲壓的關(guān)系.在此基礎(chǔ)上,得到誘導拓撲壓的變分原理.作為誘導拓撲壓的-個應(yīng)用,指出BS維數(shù)是誘導拓撲壓的特殊情形.我們還研究誘導拓撲壓的平衡測度的存在性.在第三章,我們研究在因子映射下,誘導拓撲壓之間的關(guān)系.具體地說,設(shè)π:(X,f)→(Y,g)為動力系統(tǒng)間的因子映射,也就是說π是從X到Y(jié)上與作用相容的連續(xù)滿射,我們研究動力系統(tǒng)間誘導拓撲壓的關(guān)系.作為一個應(yīng)用,我們研究BS維數(shù)的零維擴張.在第四章,從拓撲的觀念我們定義誘導測度熵,得到誘導測度熵的Katok熵公式.作為應(yīng)用,我們得到：在符號空間,誘導測度熵是測度的Hausdorff維數(shù).在第五章,我們定義可數(shù)符號空間上Markov轉(zhuǎn)移映射的幾乎可加勢的誘導Gurevich壓并且得到它的變分原理.
[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.
【學位授予單位】：南京師范大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：O19

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