动力系统中的重分形分析与大偏差

发布时间：2018-02-19 22:49

本文关键词： 拓扑熵拓扑压水平集 historic集条件变分原理大偏差非一致双曲系统　出处：《南京师范大学》2016年博士论文　论文类型：学位论文

【摘要】：设(x,d)是紧致度量空间,f：X→x为连续映射,则称(X,d,f)为拓扑动力系统。动力系统主要研究连续映射的渐进性,如拓扑熵、拓扑压、混沌和Lyapunov指数等。我们知道在经典的遍历论中的拓扑熵与测度熵是用来说明系统的复杂性的,二者之间关系称为变分原理。我们把重点放在动力系统中的非紧子集的维数熵(压)并建立条件变分原理。本文主要利用动力系统中的轨道跟踪性质来研究与Birkhoff遍历定理相关的重分形分析与大偏差性质,并将结果应用到到非一致双曲系统中去。第一章与第二章研究满足非一致Specification性质的非一致双曲系统的重分形分析。第三章,我们介绍Pesin理论,并引出Weak Shadowing Property,该性质适用于满足Pesin理论的这类非一致双曲系统。第四章与第五章,我们分别给出在Weak Shadowing Property下Birkhoff平均的水平集与发散点集的条件变分原理,同时推出了满足Limit Shadowing Property的动力系统的相应的结果。第六章主要研究Pesin理论下的大偏差性质。
[Abstract]:Let X be a compact metric space f: X. 鈫扵he dynamical system mainly studies the asymptotic properties of continuous mapping, such as topological entropy, topological pressure, topological entropy, topological pressure, topological entropy, topological pressure. We know that the topological entropy and measure entropy in classical ergodic theory are used to explain the complexity of the system. The relationship between them is called variational principle. We focus on the dimension entropy (pressure) of non-compact subset in dynamic system and establish conditional variational principle. In this paper, we mainly use the orbit tracking property in dynamic system to study and Birkhoff. Multifractal analysis and large deviation properties related to ergodic theorem, The results are applied to nonuniform hyperbolic systems. In Chapter 1 and Chapter 2, we study the multifractal analysis of nonuniform hyperbolic systems satisfying the non-uniform Specification properties. In Chapter 3, we introduce the Pesin theory. Weak Shadowing property, which is suitable for this kind of nonuniform hyperbolic systems satisfying the Pesin theory. In Chapter 4th and Chapter 5th, we give the conditional variational principles of the level set and divergent point set of Birkhoff mean in Weak Shadowing Property, respectively. At the same time, the corresponding results of the dynamical system satisfying Limit Shadowing Property are derived. Chapter 6th mainly studies the large deviation properties under the Pesin theory.
【学位授予单位】：南京师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O19

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