Mathematical Sciences: RUI - Irreducible Case of Williams Conjecture

数学科学：RUI - 威廉姆斯猜想的不可约案例

• 批准号: 9405004
• 负责人: K. Kim
• 金额: $ 5.59万
• 依托单位: Alabama State University
• 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: 1994-08-01 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9405004&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Irreducible; Case

9405004 Kim Further progress on classification of subshifts of finite type, one of the most important types of dynamical systems, seems to depend on resolving the Williams Conjecture in the irreducible case. The project focuses on this important conjecture and once this topic is resolved, an attempt will be made to find further results on classification. The method involves the use of gyration numbers to give a sort of secondary obstruction to the problem of going from a conjugacy on squares of subshifts to the original subshift. This research falls into the general area of dynamical systems. The general theory has many applications to areas such as coding theory and mathematical linguistics. A fundamental problem in dynamical systems is to determine when systems are equivalent modulo natural transformations of the base space. This work addresses the equivalence problem for the class of dynamical systems called subshifts of finite type.

小行星9405004 有限型子移位是动力系统的重要类型之一，其分类的进一步发展似乎依赖于在不可约情形下解决威廉姆斯猜想。该项目的重点是这个重要的猜想，一旦这个主题得到解决，将试图找到进一步的结果分类。该方法涉及到使用的回转数给一种次要的障碍的问题，从共轭的平方子移位到原来的子移位。 这项研究福尔斯动力系统的一般领域。一般理论在编码理论和数学语言学等领域有许多应用。动力系统中的一个基本问题是确定系统何时是基空间的等价模自然变换。这项工作解决的等价性问题的一类动力系统称为子移位有限型。