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; 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.

AbstrackMisiureWicz该项目的目的是在动态系统理论（主要是低维，既光滑又连续的研究理论中进行研究。 首席研究者将采用分析，拓扑和组合工具，以研究实际和复杂的系统。该项目的主要部分致力于研究吸引子的理性功能，树木和图的地图的旋转集，二维黄金平均转移的熵（使用用于研究一维系统的方法）以及非自治的单位动力学系统，几乎每种单程的动态系统，几乎是一种均可和一般的生物学，化学，化学，化学，化学，化学，化学，化学，化学，化学，化学，化学，化学，化学，化学，化学，化学，化学的概况，化学，化学概念很高。可以被视为动力系统的模型。有时，对该系统的研究非常困难，但是通常可以将其简化为简单，低维的研究。从数学角度来看，该项目主要致力于研究此类系统的性质。可以获得的结果通常比一般情况下要强得多。