Mathematical Sciences: Transport and Long Time Stability Dynamical Systems

数学科学：输运和长期稳定性动力系统

• 批准号: 9505017
• 负责人: H. Dumas
• 金额: $ 4万
• 依托单位: University of Cincinnati Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505017&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Transport; Long; Time

9505017 Dumas The proposed research is in the area of dynamical systems; in particular, averaging and stability of Hamiltonian systems are to be investigated. The investigator proposes to generalize Anosov's averaging theorem to systems with more general hypotheses on the driving flow; proposes to apply Lasker's frequency analysis to the study of transport in symplectic maps. Hamiltonian systems arise in celestial mechanics, accelerator physics and elsewhere in nature. The frequency analysis method, first developed by Lasker, can be applied to a variety of such systems to detect long time instability. The proposed research seeks to provide a rigorous theoretical framework for this method.

9505017大仲马 拟议的研究是在该地区的动力系统，特别是平均和稳定的哈密顿系统进行调查。调查员建议推广Anosov的平均定理系统更一般的假设上的驱动流，提出应用拉斯克的频率分析的研究运输辛地图。 哈密顿系统出现在天体力学、加速器物理学和自然界的其他地方。首先由Lasker开发的频率分析方法可以应用于各种这样的系统，以检测长时间的不稳定性。拟议的研究旨在为这种方法提供一个严格的理论框架。