Mathematical Sciences: Ergodic Theory of Symbolic Systems

林德将继续研究交换映射的动力学和符号动力学中的其他主题。林德最近发现了基于生成树的马尔可夫移位的两个不变量。这些将被进一步研究。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。我们将研究由接近多面体边界的周期点所产生的障碍物，目的是在归纳构造中使用多面体及其面。这个项目涉及遍历理论的研究。遍历理论一般关注理解系统的平均行为，其动力学过于复杂或混乱，无法在微观细节上进行跟踪。在“动力学”的标题下，可以放置关于抽象变换如何作用于光滑空间的现代理论。通过这种方式，遍历理论在寻求对均匀空间上的流动进行分类时与几何联系在一起。

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.