Mathematical Sciences: Topics in Ergodic Theory and Dynamical Systems

费尔德曼教授将继续他对遍历理论的研究，特别指出以下值得注意的领域：(I)将系统的一些等价思想从作用于群的群是整数或实数的情况推广到群只被假定为服从的情况，(Ii)光滑流形上的测地线流，和(Iii)遍历等价关系的子关系。遍历理论的研究涉及试图理解系统的平均行为，这些系统的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，可以把一组抽象的变换如何作用于光滑空间的现代理论放在下面。遍历理论中的另一个重要主题是将系统分类成在抽象意义上在数学上相同的广义范畴。费尔德曼教授的研究将与这些领域建立联系。

Professor Feldman will continue his research in ergodic theory with the following areas singled out for attention: (i) the extension of some of the ideas of equivalence of systems from the situation where the group which is acting is the integers or the reals to the case where the group is only assumed to be amenable, (ii) geodesic flows on smooth manifolds, and (iii) subrelations of ergodic equivalence relations. Research in ergodic theory involves trying to understand 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. Another important theme in ergodic theory is the classification of systems into broad categories which are mathematically identical in an abstract sense. Professor Feldman's research will make contact with these areas.