Mathematical Sciences: Topics in Ergodic Theory and Dynamical Systems

费尔德曼教授将继续他在遍历 理论，特别注意以下领域： (i)一些系统等价性思想的推广 在这种情况下， 整数或实数的情况下，该集团只假设 （ii）光滑流形上的测地线流; (iii)遍历等价关系的子关系。 遍历理论的研究包括试图理解 动力学过于复杂的系统的平均行为 或混沌的微观细节。 下 以“动力学”为标题的现代理论 抽象变换作用于光滑空间。 另一 遍历理论中的一个重要主题是 数学上完全相同的大类 在抽象的意义上。 费尔德曼教授的研究将使 与这些地区的联系。

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.