马尔科夫-戴克位移的Zeta函数和拓扑熵

关于单侧拓扑马尔可夫移位的流等价性

On flow equivalence of one-sided topological Markov shifts

我们引入的概念，暂停和流等价的单边拓扑马尔可夫移位，我们称之为单边暂停和单边流等价，分别。证明了单侧拓扑马氏位移的单侧流等价等价与连续轨道等价。我们还表明，流动的zeta函数的单面悬浮液是一个动态zeta函数与一些势函数和某些动态zeta函数的集合是不变的拓扑马尔可夫位移的单面流等价。

Motzkin位移的Zeta函数、周期点和熵

The Zeta function, Periodic Points and Entropies of the Motzkin Shift

本文讨论了一种计算子移位的zeta函数的方法，这些子移位表示为一个有限的有向图，图的标号是相应的逆半群的元素。这类子移位是作为一类性质为A的子移位（T.Hamachi，K.Inoue和W.Krieger/Subsystems of有限型and semigroupinvariants of subshifts，预印本）引入的，Dyck移位和Motzkin移位是这类子移位的代表.用这种方法还可以给出周期点和熵的确切个数，并将这些值用于有限型不可约移位嵌入到该类子移位中的嵌入条件。

Dyck 移位周期点的大偏差原理

Large deviation principles for periodic points of the Dyck shift

本文从大偏差角度研究 Dyck 移位周期点，建立以 Kolmogorov-Sinai 熵表示的二级 LDP，并刻画一级速率函数的非凸、叠加、解析及不可微性质。

关于符号动力学的某些带标签有向图

On certain labelled directed graphs of symbolic dynamics

本文针对包含 Dyck 位移的编码系统族，提出次同步化与受限复杂度概念，并显式构造扩展 Dyck 位移的次移位族，证明其可由受限复杂度和 Artin-Mazur zeta 函数等拓扑共轭不变量共同刻画。

下推自动机、图系统与C* 代数

Pushdown automata, lambda-graph systems and C*-algebras

一个$λ$ -图系统是一个带有某种附加结构的标号Bratteli图，它表示一个子移位并产生一个$C^*$ -代数.本文从下推自动机出发构造了一个$λ$ -图系统，使得该自动机所接受的语言与$λ$ -图系统所给出的子移位的可接受词的语言一致.给出了接受Markov-Dyck移位和sofic-Dyck移位语言的下推自动机的$λ$ -图系统。

One-sided topological conjugacy of normal subshifts and gauge actions on the associated $C^*$-algebras

The class of normal subshifts includes irreducible infinite topological Markov shifts, irreducible infinite sofic shifts, synchronized systems, Dyck shifts, $β$-shifts, substitution minimal shifts, and so on. We will characterize one-sided topological conjugacy classes of normal subshifts in terms of the associated $C^*$-algebras and its gauge actions with potentials.

Zeta 函数与马尔可夫过程的（线性）逻辑

Zeta Functions and the (Linear) Logic of Markov Processes

本文揭示了 zeta 函数与程序执行之间的余循环联系，并将其从图提升到动力系统，最终在所有离散时间子马尔可夫过程上构造了二阶线性逻辑的可实现性模型。

Compactness of Transfer Operators and Spectral Representation of Ruelle Zeta Functions for Super-continuous Functions

Transfer operators and Ruelle zeta functions for super-continuous functions on one-sided topological Markov shifts are considered. For every super-continuous function, we construct a Banach space on which the associated transfer operator is compact. Using this Banach space, we establish the trace formula and spectral representation of Ruelle zeta functions for a certain class of super-continuous functions. Our results include, as a special case, the classical trace formula and spectral representation for the class of locally constant functions.

On Conjugacy Invariants of $D_{\infty}$-Topological Markov Chains

A $D_{\infty}$-topological Markov chain can be represented by a pair of zero-one square matrices, which is called a flip pair. We introduce the concepts of $D_{\infty}$-strong shift equivalence and $D_{\infty}$-shift equivalence, which are equivalence relations between flip pairs. We investigate the relationships between the existence of a $D_{\infty}$-conjugacy, the existence of a $D_{\infty}$-strong shift equivalence, the existence of a $D_{\infty}$-shift equivalence and the coincidence of the Lind zeta functions.

多维映射的拟有限型、Zeta函数和符号动力学问题

Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps

我们引入了“拟有限型难题“，它是我们的拟有限型子移位的对应（发明人）。159（2005））在复杂动力学中定义的组合谜题的设置中。我们能够分析这些动态定义的熵条件相当完整，获得一个完整的分类方面的大熵措施和描述他们的措施与最大熵和周期轨道。这些结果特别适用于熵扩张映射，如（x，y）-->（1.8-x^2+ sy，1.9-y^2+sx），s很小。我们特别证明了亚纯的阿廷-马祖尔zeta函数在一个大的磁盘。这是从一个类似的新结果强正经常马尔可夫位移的亚纯半径是下界的“熵在无穷大”的图。

光滑伪阿诺索夫流的ζ函数与Fried猜想

Zeta functions and the Fried conjecture for smooth pseudo-Anosov flows

该研究针对三维流形上的光滑伪阿诺索夫流，构造了推广Anosov情形的ζ函数，证明其亚纯延拓性质、Fried猜想版本及Dirichlet类数公式的拓扑类似物，为处理奇点采用了基于马尔可夫分形的C^∞方法。

Flip Signatures

A $D_{\infty}$-topological Markov chain is a topological Markov chain provided with an action of the infinite dihedral group $D_{\infty}$. It is defined by two zero-one square matrices $A$ and $J$ satisfying $AJ=JA^{\textsf{T}}$ and $J^2=I$. Flip signature is obtained from symmetric bilinear forms with respect to $J$ on the eventual kernel of $A$. We modify Williams' decomposition theorem to prove flip signature is a $D_{\infty}$-conjugacy invariant. We introduce natural $D_{\infty}$-actions on Ashley's eight-by-eight and the full two-shift. The Flip signatures show that Ashley's eight-by-eigh…