Mathematical Sciences: Flow Equivalence of Subshifts

数学科学：子移流等价

• 批准号: 9401079
• 负责人: Danrun Huang
• 金额: $ 5.36万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-15 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401079&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Flow; Equivalence; Subshifts

9401079 Huang The proposer has classified up to flow equivalence all 2- component shifts of finite type. He has recently classified n-component shifts of finite type when 1 is not an eigenvalue of the defining matrix. The project is to complete the classification for general n-component shifts of finite type by proving a crucial "two-sided" realization theorem which may also have a new implication to C*-algebras. Moreover, based on the existing results, the proposer intends to study (almost) flow equivalence of sofic shifts, of stochastic Markov shifts and of the more general setting of Laurent polynomial matrices. Especially, he plans to explore more interesting relations between flow equivalence and C*-algebras, including a conjecture he made for the classification of non-simple Cuntz-Krieger algebras associated to 2-component shifts of finite type. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading of "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry and algebra in their quests to clasify flows and algebraic structures. ***

小行星9401079 提出者把所有有限型二分量移位分类到流等价。他最近将 当1不是定义矩阵的特征值时，有限类型的n分量移位。本课题的目的是完成有限型一般n分量移位的分类， 证明了一个关键的“双侧”实现定理， 对C*-代数有一个新的含义。而且看 现有的结果，提议者打算研究（几乎）流 等价的sofic移位，随机马尔可夫移位和更一般的设置洛朗多项式矩阵。 特别是，他计划探索流等价和C*-代数之间更有趣的关系，包括他为与有限型2分量移位相关的非简单Cuntz-Krieger代数的分类所做的猜想。 这个项目涉及遍历理论的研究。遍历理论一般涉及理解系统的平均行为，其动力学过于复杂或混乱，以至于无法在微观细节中遵循。在“动力学”的标题下，可以放置抽象变换群如何作用于光滑空间的现代理论。遍历理论以这种方式与几何学和代数学接触，以寻求对流和代数结构进行分类。 ***