Low-Dimensional Dynamical Systems

低维动力系统

• 批准号: 9970543
• 负责人: Michal Misiurewicz
• 金额: $ 7.46万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970543&HistoricalAwards=false
• 关键词: Low; Dimensional; Dynamical; Systems

AbstractMisiurewiczThe objective of the project is to perform research in the theory of dynamical systems, mainly low-dimensional, both smooth and continuous. The Principal Investigator will apply analytical, topological and combinatorial tools in order to investigate real and complex systems. The main parts of the project are devoted to the study of the attractors for rational functions, rotation sets for maps of trees and graphs, entropy of the 2-dimensional golden mean shift (using methods developed for studying one-dimensional systems), and nonautonomous discrete dynamical systems, both low-dimensional and general.For almost every phenomenon from Physics, Chemistry, Biology, Medicine, Economy and other sciences one can make a mathematical model that can be regarded as a dynamical system. Sometimes the study of this system is extremely difficult, but quite often it can be reduced to the study of a much simpler, low dimensional one. This project is devoted mainly to the investigation of the properties of this type of systems from the mathematical point of view. The results that can be obtained are usually much stronger than in the general case.

AbstractMisiurewicz 该项目的目标是进行动力系统理论的研究，主要是低维、光滑和连续的系统。 首席研究员将应用分析、拓扑和组合工具来研究真实和复杂的系统。该项目的主要部分致力于研究有理函数的吸引子、树和图的旋转集、二维黄金均值位移的熵（使用为研究一维系统而开发的方法）以及非自治离散动力系统，无论是低维的还是一般的。对于物理、化学、生物、医学、经济和其他科学中的几乎每一种现象，我们都可以建立一个可以被视为动力系统的数学模型。有时，对这个系统的研究极其困难，但通常可以将其简化为对一个更简单、低维系统的研究。该项目主要致力于从数学角度研究此类系统的特性。可以获得的结果通常比一般情况下强得多。