Periodic orbits of Hamiltonian systems and symplectic reduction
Periodic orbits of Hamiltonian systems and symplectic reduction
复制标题
哈密顿系统的周期轨道和辛约简
DOI：
10.1088/0305-4470/29/3/018
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
C. M. Ontalba
中科院分区：
文献类型：
--
作者：
Alberto Ibort;C. M. Ontalba
讨论了对称哈密顿系统的相对周期轨道的概念，建立了约简哈密顿系统周期轨道与未约简哈密顿系统周期轨道的对应关系。从环空间的辛约简的角度研究了具有对称性的变分原理，得到了用限制在未约简流形的环空间的子流形上的作用泛函的临界子集来表征约简周期轨道的方法。最后，作为一个应用，证明了如果辛形式具有有限积分秩，则辛流形上哈密顿系统的周期轨道具有变分刻划。
The notion of relative periodic orbits for Hamiltonian systems with symmetry is discussed and a correspondence between periodic orbits of reduced and unreduced Hamiltonian systems is established. Variational principles with symmetries are studied from the point of view of symplectic reduction of the space of loops, leading to a characterization of reduced periodic orbits by means of the critical subsets of an action functional restricted to a submanifold of the loop space of the unreduced manifold. Finally, as an application, it is shown that if the symplectic form has finite integral rank, then the periodic orbits of a Hamiltonian system on the symplectic manifold admit a variational characterization.