Stability in Steller Dynamics and Bifurcation in Symmetric Hamiltonian Systems

8901645 Wan 主要研究者将研究 恒星动力学中的平衡点和抽象的分岔 具有一定对称性的哈密顿系统。 对于无碰撞球形系统的稳定性问题， 首席研究员打算修改所谓的 能量Casimir方法在其哈密顿设置，以便 包括不平等限制。 该方法已被证明 成功解决流体和等离子体的稳定性问题。 的 当前的目标是建立非线性稳定性， 某些球对称平衡， 安东诺夫以前研究过。 受涡动力学最新研究成果的启发， 首席研究员还计划分析稳定性， 平衡点和周期轨道的分支 哈密顿系统（带反转）。 特别强调 将被放置在稳定性计算和所扮演的角色 通过这些系统的可逆性，在对称性的存在下。 非线性稳定性问题是 恒星动力学的重要性。 结果可用于 解释球状星系和球状星星的出现 集群 对称哈密顿系统的结果将是 适用于广泛的物理系统， 相同的对称结构。

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.