Stability in Steller Dynamics and Bifurcation in Symmetric Hamiltonian Systems

Steller 动力学的稳定性和对称哈密顿系统的分岔

• 批准号: 8901645
• 负责人: Yieh-Hei Wan
• 金额: $ 5.23万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901645&HistoricalAwards=false
• 关键词: Stability; Steller; Dynamics; Bifurcation; Symmetric

8901645 Wan The principal investigator will study the stability of equilibria in stellar dynamics and bifurcation in abstract Hamiltonian systems which possess certain symmetry. For stability problems in collisionless spherical systems, the principal investigator intends to modify the so-called energy-Casimir method in its Hamiltonian setting so as to include inequality constraints. This method has been proven to be successful in stability problems of fluids and plasmas. The immediate goal is to establish the nonlinear stability of certain spherically symmetric equilibria which have been studied previously by Antonov. Motivated by recent results on vortex dynamics the principal investigator also plans to analyze the stability and bifurcation of equilibria and periodic orbits in a symmetric Hamiltonian system (with a reversion). Particular emphasis will be placed on stability computations and on the role played by reversibility of these systems, in the presence of symmetry. Nonlinear stability questions are of fundamental importance in stellar dynamics. The results may be used to explain the appearance of spherical galaxies and globular star clusters. Results on symmetric Hamiltonian systems will be applicable to a wide range of physical systems possessing the same underlying symmetry structure.

8901645万首席研究员将研究具有一定对称性的抽象哈密顿系统中恒星动力学平衡的稳定性和分岔问题。对于无碰撞球面系统的稳定性问题，首席研究员打算修改所谓的能量-卡西米尔方法在其哈密顿量设置中，以包含不等式约束。该方法已被证明在流体和等离子体的稳定性问题上是成功的。当前的目标是建立安东诺夫先前研究过的某些球对称平衡的非线性稳定性。受最近关于涡旋动力学的研究结果的启发，首席研究员还计划分析对称哈密顿系统（带反转）中平衡态和周期轨道的稳定性和分岔。特别强调的是稳定性计算和在对称性存在下这些系统的可逆性所起的作用。非线性稳定性问题在恒星动力学中具有重要的基础意义。这些结果可以用来解释球状星系和球状星团的出现。关于对称哈密顿系统的结果将适用于具有相同底层对称结构的广泛物理系统。