Mathematical Sciences: Topics in Dynamical Systems and Differential Geometry

这是一个遍历数学研究项目 理论与动力系统 这些领域的总主题 是研究从长期来看， 在逐步迭代或连续迭代下的空间变换 流 三位主要研究人员希望他们的工作 从协作互动中受益。 对应于什么样的底层空间， 题材大致分为三类：象征性的， 平滑和可测量的动态。 符号学研究课题 动力学是移位的自同构， 马尔可夫位移和非负积分矩阵。 在光滑 动力学，主题包括研究动力学的动力学方法 Navier-Stokes方程，随机同态和 误差的传播，测地线流和黎曼 几何 在可测量动力学领域， 包括受限轨道等价和平铺表示 更高维度的真实的行为。

This is a project for mathematical research in ergodic theory and dynamical systems. The general theme of these areas is to study the average behavior, over the long run, of transformations of a space under stepwise iteration or continuous flow. The three principal investigators expect their work to benefit from collaborative interactions. Corresponding to what sort of underlying space one has, the subject matter divides roughly into three categories: symbolic, smooth, and measurable dynamics. Research topics in symbolic dynamics are automorphisms of the shift, regular isomorphism of Markov shifts, and nonnegative integral matrices. In smooth dynamics, topics include dynamical methods in the study of the Navier - Stokes equation, random diffeomorphisms and the propagation of roundoff error, and geodesic flows and Riemannian geometry. In the area of measurable dynamics, research topics include restricted orbit equivalence and tiling representations of higher dimensional real actions.