Classification and Invariants of Subshifts

子移的分类和不变量

• 批准号: 9900265
• 负责人: K. Kim
• 金额: $ 13.07万
• 依托单位: Alabama State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-06-01 至 2002-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9900265&HistoricalAwards=false
• 关键词: Classification; Invariants; Subshifts

AbstractKim/RoushFor a long time the Williams conjecture that shift equivalence is the same as strong shift equivalence was the dominant approach to classifying subshifts of finite type. With our negative resolution of this conjecture, the way is open to either determine that the invariants involved in that proof are a complete set, or to find new invariants and algorithms to effectively classify subshifts of finite type up to topological conjugacy. We will consider group-theoretic, cohomological, and other methods. We will also try to answer some questions raised by Nasu on his textile systems (already partly solved by Boyle and Maass).Nontechnical description: Symbolic dynamics is a mathematical theory that can handle strings of symbols that can arise in many connections. It has been used to formulate codes for efficient computer data storage and transmission. It is an important and fundamental part of dynamical systems theory, which studies how systems (which might be something like the solar system, the earth's atmosphere, or the human body) change under time. Symbolic dynamics has been applied to topological quantum field theory, which establishes a link to modern physics, and also to other important areas of mathematics such as the theory of knots. The present proposal is primarily a project to classify subshifts of finite type, which are the most extensively studied kind of symbolic dynamical system.

长期以来，威廉姆斯猜想（移位等价与强移位等价相同）是有限型子移位分类的主要方法。 随着我们对这个猜想的否定解决，要么确定该证明中涉及的不变量是一个完整的集合，要么找到新的不变量和算法来有效地将有限类型的子移位分类到拓扑共轭。 我们将考虑群论、上同调和其他方法。 我们还将尝试回答那须对他的纺织系统提出的一些问题（波义耳和马斯已经部分解决了这些问题）。非技术性描述：符号动力学是一种数学理论，可以处理在许多连接中可能出现的符号串。 它已被用来制定有效的计算机数据存储和传输的代码。 它是动力系统理论的一个重要和基本部分，研究系统（可能是太阳系，地球大气层或人体）如何随时间变化。 符号动力学被应用于拓扑量子场论，建立了与现代物理学的联系，也与其他重要的数学领域如纽结理论建立了联系。 目前的建议主要是一个项目，分类子移位有限型，这是最广泛的研究种符号动力系统。