Mathematical Sciences: Ordered and Chaotic Motions in Hamiltonian Systems

数学科学：哈密顿系统中的有序运动和混沌运动

• 批准号: 8802118
• 负责人: Clarence Wayne
• 金额: $ 4.39万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802118&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Ordered; Chaotic; Motions

This project is devoted to the study of regular and chaotic motion in nearly integrable infinite dimensional hamiltonian systems. Such systems include certain nonlinear partial differential equations, the wave and vibrating beam equations for instance. Statistical mechanics and condensed matter physics also lead to these systems. The approach consists of extending KAM theory to perturbations of completely integrable hamiltonian systems. Together with the usual methods of the calculus of variation and bifurcation analysis, KAM theory will shed new light on the existence of periodic and quasiperiodic solutions. In addition, geometric and numerical methods will be employed.

该项目致力于研究几乎可以整合的无限尺寸哈密顿系统中的常规和混沌运动。 这样的系统包括某些非线性偏微分方程，例如波和振动梁方程。 统计力学和凝结物理学也导致了这些系统。 该方法包括将KAM理论扩展到完全可以整合的哈密顿系统的扰动。 加上变异和分叉分析的计算的通常方法，KAM理论将为周期性和准二体溶液的存在提供新的启示。 另外，将采用几何方法和数值方法。