Mathematical Sciences: Recurrence, Averaging and Entropy in Ergodic Theory

这个项目跨越了遍历理论的各个领域。 Bergelson教授将专注于研究多种 动力系统中的递归和混合。 存在的问题 研究与组合数学和数论密切相关。 罗森布拉特教授的研究将在该地区几乎 各种平均方法的处处收敛性。 这个奖项 还将支持博士后研究员沃德博士。 他的工作 涉及到正熵，混合所有 命令，指数递归，和整数的作用 紧群上的格 因为动力系统可以表现出极其复杂的， 即使是混乱的行为，也不可能遵循时间 这样一个系统的开发过程非常详细。 遍历理论 包括研究这些物质的某些平均性质的方法， 系统包含足够的信息，但仍然是有用的。

This project spans a variety of fields in ergodic theory. Professor Bergelson will concentrate on the study of multiple recurrence and mixing in dynamical systems. The problems to be researched are closely related to combinatorics and number theory. Professor Rosenblatt research will be in the area of almost everywhere convergence of various averaging methods. This award will also support Dr. Ward, a postdoctoral researcher. His work involves the relationship between positive entropy, mixing of all orders, exponential recurrence, and the action of the integer lattice on compact groups. Because dynamical systems can display extremely complicated, even chaotic behavior, it is impossible to follow the time development of such a system in complete detail. Ergodic theory involves methods of studying certain average properties of these systems which contain enough information to nevertheless be useful.