Mathematical Sciences: Equivalence Relations of Measurable Dynamical Systems

数学科学：可测量动力系统的等价关系

• 批准号: 9501103
• 负责人: Ayse Sahin
• 金额: $ 5.03万
• 依托单位: North Dakota State University Fargo
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501103&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Equivalence; Relations; Measurable

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. ***

小行星9501103 拟议的研究集中在可衡量的动态领域。特别是，它建议研究可测动力系统的多维时间参数。考虑的一些主题是基于平铺的动力系统和限制轨道等价。每个多维连续时间动力系统都可以表示为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。本研究将探讨离散动力系统之间的内在关系所产生的不同表示的一个固定的连续时间系统。 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。它们也使抽象的可测量动力学问题成为具体的平铺几何问题成为可能。这项调查将深入了解其中一些联系。此外，本文提出的方法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序列逼近方法。 ***