Mathematical Sciences: Equivalence Relations of Measurable Dynamical Systems

[501103]沙欣提议的研究集中在可测量动力学领域。特别提出了对具有多维时间参数的可测动力系统的研究。考虑的一些主题是基于平铺的动力系统和受限轨道等效。每一个多维连续时间动力系统都可以表示为一个基于平铺的动力系统。每个这样的表示都有一个自然的离散时间动力系统。本研究将探讨由固定连续时间系统的不同表示所产生的离散动力系统之间的内在关系。基于平铺的问题本身就很有趣。它们提供了晶体学、多维连续时间和离散时间动力系统之间的联系。它们也使得将抽象的可测量动力学问题作为具体的平铺几何问题成为可能。本调查将深入了解其中的一些联系。此外，本文提出的方法还引入了一种新的一步构造技术。这种方法不同于传统的用于研究高维动力系统的顺序逼近方法。＊＊＊

9501103 Sahin The proposed research concentrates on areas in measurable dynamics. In particular, it is proposed to study measurable dynamical systems with multidimensional time parameters. Some of the topics considered are tiling based dynamical systems and restricted orbit equivalences. Every multidimensional continuous-time dynamical system can be represented as a tiling based dynamical system. There is a natural discrete-time dynamical system associated to each such representation. This investigation will explore the intrinsic relationship between discrete dynamical systems arising from different representations of a fixed continuous-time system. Tiling based problems are interesting in their own right. They provide a link between crystallography, multidimensional continuous-time and discrete-time dynamical systems. They also make it possible to pose problems of abstract measurable dynamics as concrete tiling geometry questions. This investigation will provide insight into some of these connections. In addition, the method proposed here introduces a new one-step constructive technique. This technique differs from the traditional sequential approximation techniques used in studying higher dimensional dynamical systems. ***