Mathematical Sciences: Ergodic Theory of Symbolic Systems

林德将继续他的调查动态， 交换映射和符号动力学中的其他主题。 Lind 最近发现两个不变量的马尔可夫转移的基础上， 生成树 将进一步研究这些问题。 通塞尔计划 继续研究马尔可夫的结构和分类 链和相关的积极性问题。 产生的障碍 从接近多面体边界的周期点 将研究的目的是使用多面体和它的脸 在归纳结构中。 这个项目涉及遍历理论的研究。 遍历 理论一般涉及理解的平均行为， 系统的动力学过于复杂或混乱， 在微观细节上进行跟踪。 在“动态”标题下， 可以把现代理论放在抽象的 变换作用于光滑空间。 这样遍历理论 与几何学接触，以寻求对 齐性空间

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.