Mathematical Sciences: Topics in Dynamical Systems and Differential Geometry

该奖项将支持三项研究活动 调查人员在几个领域的象征性，顺利，和可衡量的 动力学 符号动力学的主题之一是自同构 非负矩阵的逆问题，以及 一般结构性问题。 在平滑动力学中， 主题是遍历性和拓扑传递性的部分 双曲动力系统，测地流，奇异空间 非正曲率。 在研究的主题中， 可测动力学是受限轨道等价的，非奇异的 合理的拼接，自然流畅的施工 可测量系统的模型。 这个研究小组将研究动力系统。概念 是一个非常普遍的问题。 我的想法是 系统必须以某种方式随时间演变。 目的是学习 关于动力学的一般性质的东西， 分类这些系统的大家庭。 动力系统 通常在很长一段时间内表现得很混乱 即使它们是完全可预测的。 了解 然而，在这种情况下，如何提取知识是一个 当今科学面临的最大问题。 这是其中一 动力系统研究的终极目标。

This award will support the research activities of three investigators in several areas of symbolic, smooth, and measurable dynamics. Among the topics in symbolic dynamics are automorphisms of the shift, inverse problems for non-negative matrices, and general structural questions. In smooth dynamics some of the topics are ergodicity and topological transitivity of partially hyperbolic dynamical systems, geodesic flows, and singular spaces of non-positive curvature. Among the topics to be studied in measurable dynamics are restricted orbit equivalence, non-singular and rational joinings, and the construction of natural smooth models of measurable systems. This research group will study dynamical systems. The notion of a dynamical system is a very general one. The idea is just that the system must evolve in time in some way. The object is to learn things of a general nature about the dynamics in the hope of classifying large families of these systems. The dynamical systems under consideration often behave chaotically over large time periods even when they are completely predictable. To understand how nevertheless to extract knowledge in this case is one of the most important problems facing science today. This is one of the ultimate goals in the study of dynamical systems.