Mathematical Sciences: Construction and Convergence in Ergodic Theory

霍金斯、彼得森和维尔德尔将继续调查 几乎处处收敛的微妙现象， 遍历理论，涉及合并无数 异常的零度量集变成一个坏的度量集 零，即连续参数平稳随机抽样 随机交换的过程和遍历定理 地图 一种描述随机 遍历平均总是收敛几乎在任何地方， 随机遍历定理的一个强大的扩展，也将 推广了Bourgain，Furstenberg， 卡茨尼尔森和奥恩斯坦 该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

Hawkins, Petersen, and Wierdl will continue to investigate subtle phenomena in the area of almost everywhere convergence in ergodic theory which involve coalescing uncountably many exceptional sets of measure zero into a single bad set of measure zero, namely random sampling of continuous-parameter stationary processes and ergodic theorems for randomly applied commuting maps. A characterization of situations in which the random ergodic averages always converge almost everywhere would provide a powerful extension of the Random Ergodic Theorem and would also generalize the return times theorem of Bourgain, Furstenberg, Katznelson, and Ornstein. 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.