Hamiltonian dynamics and infinte-dimensional Lie groups

哈密​​顿动力学和无限维李群

• 批准号: 194132-2009
• 负责人: Khesin, Boris
• 金额: $ 2.33万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=476588
• 关键词: Hamiltonian; dynamics; infinte; dimensional; Lie

Groups of symmetries emphasize invariance of structures in mathematics similarly to what symmetry means in an everyday sense. Many groups arising in physics and mathematics are infinite-dimensional. The main objective of the proposal is to find a closer link between infinite-dimensional groups, the associated with them variational principles, their geometry, and the dynamical systems with infinitely many degrees of freedom. Such links have proved to be important for applications in many areas of science ranging from quantum mechanics to meteorology. The two long-term objectives of the proposal are:

对称群强调数学中结构的不变性，类似于对称在日常意义上的含义。物理学和数学中出现的许多群都是无限维的。该提案的主要目标是找到无限维群之间的更紧密联系，与之相关的变分原理，几何学和具有无限多个自由度的动力系统。事实证明，这种联系对于从量子力学到气象学的许多科学领域的应用都很重要。 该提案的两个长期目标是：