【摘要】：本文分為兩部分,探討動力系統(tǒng)中因子映射的packing壓的半共軛公式和重分形分析中的packing熵的條件變分原理.第一部分定義次可加勢函數(shù)族的packing拓?fù)鋲?上容量拓?fù)鋲?并給出次可加勢函數(shù)族的packing壓的兩個半共軛公式.第二部分?jǐn)⑹隽酥胤中畏治鲋械幕局R并在弱specification性質(zhì)下,證明了packing熵的條件變分原理.論文的大致框架如下：第一章,介紹了拓?fù)潇?拓?fù)鋲汉椭胤中畏治龅谋尘?第二章,介紹了動力系統(tǒng)與遍歷論理論中的一些基本概念及結(jié)果.第三章,定義了次可加勢函數(shù)族的幾種拓?fù)鋲?并給出次可加勢函數(shù)族的packing壓的半共軛公式.第四章,敘述了重分形中的一些定義和結(jié)論,并得到了packing熵的條件變分原理.
[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.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O19

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相關(guān)期刊論文 前1條

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本文編號：2434706