Mathematical Sciences: Transport for Symplectic Mapping

数学科学：辛映射的传输

• 批准号: 9001103
• 负责人: James Meiss
• 金额: $ 6.08万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001103&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Transport; Symplectic; Mapping

This project will study transport phenomena in symplectic mappings of four or more dimensions. The goal is to partition phase space into regions bounded by partial barriers through which flux occurs. A candidate for such a region is a resonance, defined as a volume in the neighborhood of an elliptic point; its boundary will be obtained from limits of librational periodic orbits. Resonance volumes will be computed and we will determine whether resonances partition phase space. The correlation function for orbits in the neighborhood of a resonance boundary well be studied to determine whether the series for the diffusion tensor converges. Transport will be defined in terms of the flux across resonance boundaries, including branching ratios for transitions from one resonance to a neighboring one, as well as drift along a commensurability channel. To compute the latter a restricted symplectic map will be introduced and studied. Numerical techniques will include frequency filtering and finding periodic orbits.

该项目将研究四个或更多维度的符号映射中的运输现象。 目的是将相位空间划分为通过发生通量发生的部分屏障界定的区域。 这种区域的候选者是共鸣，被定义为椭圆点附近的体积。它的边界将从库周期轨道的限制中获得。 将计算共振量，我们将确定共振分区相位空间是否。 井井有条，以确定扩散张量的系列是否收敛，孔口的轨道的相关函数。 运输将根据跨共振边界的通量来定义，包括从一个共振到相邻谐振的分支比率，以及沿着相当性通道的漂移。 为了计算后者，将引入和研究受限制的符号图。 数值技术将包括频率过滤和查找周期轨道。