Mathematical Sciences: Planar Dynamical Systems

数学科学：平面动力系统

• 批准号: 9302986
• 负责人: Robert Devaney
• 金额: --
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302986&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Planar; Dynamical; Systems

The goal of this research is to investigate the chaotic behavior of several important types of dynamical systems. The systems involved in the study include several classes of complex dynamical systems, namely the exponential and the standard family, an important class of systems arising in physics. The investigation will also involve several related families, including area-preserving and piecewise linear maps. Finally, the tricorn, an important new fractal structure, will be described.

本研究的目的是研究几种重要类型的动力系统的混沌行为。研究中涉及的系统包括几类复杂的动力系统，即指数和标准族，这是物理学中出现的一类重要系统。研究还将涉及几个相关的家庭，包括面积保持和分段线性映射。最后，三角形，一个重要的新的分形结构，将被描述。