极小动力系统与近似共轭

极小同胚与测度上的近似共轭

Minimal Homeomorphisms and Approximate Conjugacy in Measure

设X是具有有限覆盖维的无限紧度量空间。设$\afhpa,\bt: X\to X$是两个极小同胚.设两个交叉积C* 代数s的$K_0$ -群的值域在实仿射连续函数空间中稠密.证明了$\af$和$\bt$在测度上一致近似共轭当且仅当它们具有仿射同胚不变概率测度空间.

Furstenberg变换与近似共轭

Furstenberg Transformations and Approximate Conjugacy

设$α$和$β$是2-环面上与无理数$θ_1,$ $θ_2,$整数$d_1, d_2$和Lipschitz函数$f_1$和$f_2.$有关的两个Furstenberg变换，我们证明了$α$和$β$在测度理论意义下近似共轭，如果（且仅当）$\R/\Z.$中的$\bar{θ_1\pm θ_2}=0$与简单顺从$C^*$ -代数的分类密切相关，证明了$α$和$β$是近似$K$ -共轭的当（且仅当）$\bar{θ_1\pm θ_2}=0$在$\R/\Z$和$|d_1|=|d_2|.$中。这也等价于相关的交叉积$C^*$ -代数是同构的。

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.

Approximate $K$-conjugacies and $C^*$-approximate conjugacies of minimal dynamical systems

In this article, we extend H. Matui and H. Lin's notions of approximate $K$-conjugacies and $C^*$-strongly approximate conjugacies to general minimal dynamical systems. In particular, upon modifying a result of the existence of minimal skew products, we answer a question of H. Lin and show that, associated with any Cantor minimal system $(K,\tildeα)$, there is a class $R_0(\tildeα)$ of minimal skew products on $K\timesΩ$, such that for any two rigid homeomorphisms $α\in R_0(\tildeα)$ and $β\in R_0(\tildeβ)$, the notions of approximate $K$-conjugacy and $C^*$-strongly approximate conjugacy coin…

On a categorical framework for classifying C*-dynamics up to cocycle conjugacy

We provide the rigorous foundations for a categorical approach to the classification of C*-dynamics up to cocycle conjugacy. Given a locally compact group $G$, we consider a category of (twisted) $G$-C*-algebras, where morphisms between two objects are allowed to be equivariant maps or exterior equivalences, which leads to the concept of so-called cocycle morphisms. An isomorphism in this category is precisely a cocycle conjugacy in the known sense. We show that this category allows sequential inductive limits, and that some known functors on the usual category of $G$-C*-algebras extend. After…

迹秩为1的单$C^*$ -代数中的Kishimoto共轭定理

Kishimoto's Conjugacy Theorems in simple $C^*$-algebras of tracial rank one

设$A$是一个满足泛系数定理（UCT）的有限迹秩有单位可分单顺从$C^*$ -代数.假设$\af$和$\bt$是两个具有Rokhlin性质的自同构，{诱导对$A$的$K$ -理论数据的相同作用。}证明了$\af$和$\bt$是强上循环共轭和一致近似共轭的，即存在一个酉序列$\{u_n\}\subset A$和一个强渐近内自同构序列$σ_n$使得$$ \af={\rm Ad}\, u_n\circ σ_n\circ \bt\circ σ_n^{-1}\andeqn \lim_{n\to\infty}\|u_n-1\|=0, $$和逆成立. {We然后给出了一个$K$理论的描述，至少在一个温和的限制下，确切地说，当$\af$和$\bt$是上循环共轭。此外，我们表明，任何$K$ -理论数据，存在一个自同构$\af$与Rokhlin属性，它具有相同的$K$ -理论数据。