Mathematical Sciences: Dynamical Systems with Infinitely Many Degrees of Freedom in Mathematical Physics

数学科学：数学物理中具有无限多个自由度的动力系统

• 批准号: 9203359
• 负责人: Clarence Wayne
• 金额: $ 7.5万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203359&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamical; Systems; Infinitely

This proposal is concerned with the dynamics of some partial differential equations that arise in mathematical physics. Problems concerning the method of accelerated convergence, KAM theory, center manifolds, and normal forms are complicated in the finite dimensional case. In infinite dimensions there are additional complications such as the appearance of zero divisors rather that just small divisors. Dynamical systems is a geometric rigorous way of describing the behavior of solutions of systems of ordinary or partial differential equations which can not be solved explicitly. The ability to accurately describe the behavior of such solutions has important ramifications in understanding the world around us.

这个建议涉及到一些局部的动力学 数学物理中的微分方程。 关于加速收敛法的几个问题 理论，中心流形，和规范形式是复杂的， 有限维情形 在无限的维度里 额外的复杂性，如零因子的出现 而不是小除数。 动力学系统是一种严格的几何描述方法 常微分方程组或偏微分方程组解的性质 不能显式求解的微分方程。 的 准确描述这种解决方案的行为的能力 对理解我们周围的世界有着重要的影响。