Mathematical Sciences: Ergodic Theory and Combinatorics

Ornstein和Katznelson将调查 以下领域：圆的群同态， “圆技术”在扭曲图中的应用;统计 稳定性;熵;收益率和数据压缩;伯努利 系统;组合学中的遍历和拓扑动力学方法 特别是确定的特征因素 给定指数多项式的遍历系统和正则性 分形映射的性质。 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

Ornstein and Katznelson will investigate problems in the following areas: Groups of diffeomorphisms of the circle, application of "circle techniques" to twist maps; statistical stability; entropy, returns rates and data compression; Bernoulli systems; ergodic and topological dynamic methods in combinatorics and in particular identifying the characteristic factors of ergodic systems for given exponent polynomials; and regularity properties for maps of fractals. 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.