Mathematical Sciences: Dynamical Systems and Applications

数学科学：动力系统及其应用

• 批准号: 9207069
• 负责人: Shui-Nee Chow
• 金额: $ 2.86万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1994-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207069&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamical; Systems; Applications

The principal investigator will develop and improve methods for understanding bifurcation from invariant tori, semi-linear elliptic problems in unbounded domains, and singularly perturbed differentiable systems. The underlying technique is the theory of invariant manifolds. Dynamical systems encompass both ordinary and partial differential equations, expressing a geometric approach to the study of such equations. An understanding of invariant manifolds is extremely critical as it gives a great deal of information about behavior of solutions in a neighborhood of special solutions.

主要研究者将发展和改进从不变环面、无界域的半线性椭圆问题和奇摄动可微系统中理解分岔的方法。基本技术是不变流形理论。动力系统包括常微分方程和偏微分方程，表达了研究这些方程的几何方法。对不变流形的理解是非常重要的，因为它提供了大量关于解在特解的邻域内的行为的信息。