Stability in Steller Dynamics and Bifurcation in Symmetric Hamiltonian Systems

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的恒星动力学平衡点的稳定性和分叉。对于无碰撞球面系统的稳定性问题，主要研究人员打算在哈密顿环境下对所谓的能量-Casimir方法进行修改，以便包含不等式约束。这种方法在流体和等离子体的稳定性问题上已被证明是成功的。近期的目标是建立安东诺夫以前研究过的某些球对称平衡点的非线性稳定性。受涡旋动力学最新结果的启发，首席研究员还计划分析对称哈密顿系统(带有反转)的平衡轨道和周期轨道的稳定性和分叉。我们将特别强调稳定性的计算，以及在存在对称性的情况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意义。这一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基本对称结构的广泛的物理系统。

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.