Birkhoff平均的重分形分析和可数群作用Bowen拓扑熵

发布时间：2018-03-15 23:37

本文选题：拓扑熵　切入点：拓扑压　出处：《南京师范大学》2017年博士论文　论文类型：学位论文

【摘要】：本文致力于研究动力系统中Birkhoff平均的重分形分析和可数离散群作用的Bowen拓扑熵。(X,d,f)称为拓扑动力系统,是指(X,d)是一个紧致度量空间,f是一个X到自身的连续映射。第一章到第三章,我们研究了具有几乎弱specification性质的映射并且把结果应用到紧致度量阿贝尔群的遍历自同构。我们研究了historic集的压、generic性质,并且得到了关于集合E(I)拓扑压的一个条件变分原理,其中.在第四章,我们对具有gluing orbit性质的映射证明了关于水平集拓扑熵的一个变分原理,其中水平集形式为这样的结果可以应用到拓扑可迁的有限型子位移和测地度量空间的测地流。在第五章,我们定义了可数群作用下Bowen拓扑熵、测度熵,并且建立了关于Bowen拓扑熵和Brin-Katok测度熵的变分原理。本章中的方法也可以应用到序列熵、有限生成半群、离散非自治动力系统等。
[Abstract]:This paper is devoted to the study of the multifractal analysis of Birkhoff mean and the Bowen topological entropy of countable discrete groups in dynamical systems, which are called topological dynamical systems. Is a compact metric space f is a continuous mapping from X to itself. We study the mapping with almost weak specification property and apply the result to the ergodic automorphism of compact metric Abelian group. We study the compactness generic property of historic set and obtain a conditional variational principle for topological pressure of historic set. In Chapter 4th, we prove a variational principle about topological entropy of level set for mapping with gluing orbit property. In chapter 5th, we define the topological entropy and measure entropy of Bowen under countable group action, which can be applied to topologically transitive finite type subdisplacement and geodesic flow in geodesic space. The variational principles of Bowen topological entropy and Brin-Katok measure entropy are established. The methods in this chapter can also be applied to sequence entropy, finitely generated Semigroups, discrete nonautonomous dynamical systems and so on.
【学位授予单位】：南京师范大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O189

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