Mathematical Sciences: Ergodic Theory of Symbolic Systems

林德将继续研究通勤映射的动力学和符号动力学的其他主题。Lind最近发现了基于生成树的马尔可夫转移的两个不变量。这些都将得到进一步的研究。Tuncel计划继续研究马尔可夫链的结构和分类以及相关的正性问题。将研究由接近多面体边界的周期点引起的障碍物，目的是在归纳结构中使用多面体及其面。这个项目涉及对遍历理论的研究。一般说来，遍历理论涉及理解系统的平均行为，这些系统的动力学太复杂或太混乱，以至于无法在微观细节上进行跟踪。在标题“动力学可以被放在现代理论如何抽象变换如何作用于光滑空间。这样，遍历理论与几何联系起来，寻求在均匀空间上对流动进行分类。

Lind will continue his investigations of the dynamics of commuting mappings and other topics in symbolic dynamics. Lind has recently found two invariants of Markov shifts based on spanning trees. These will be further studied. Tuncel plans to continue his study of the structure and classifications of Markov chains and related positivity problems. Obstructions arising from periodic points approaching the boundary of the polytope will be studied with the aim of using the polytope and its faces in an inductive construction. 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 "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 in its quest to classify flows on homogeneous spaces.