Hamilton系统的大范围周期轨道的估计

Hamilton系统的相轨道位于正则值所确定的等能曲面上,而系统的大范围周期轨道可以代表等能曲面的同调类,这些同调类一般非平凡.而等能曲面的拓扑性质又由相空间的拓扑性质和Hamilton函数的大尺度性质决定,用这两种性质估算了受外力的刚体运动的等能曲面的第1同调群的秩.用同伦论、同调论和Morse理论把已有证明中的不足之处加以改进,得出基本定理的新的证明.

Estimation of Large-Scale Periodic Orbits in Hamiltonian System

The phase orbits of a Hamiltonian system are on the equi-energy level surface which is determined by the regular value.The largescale periodic orbits of the system can represent the homology classes,which are generally nontrivial,on the equi-energy level surface and the topological properties of the equi-energy level surface are determined by that of the phase space and the largescale properties of Hamiltonian function.These properties were used for estimation of the rank of the first homology group of the equi-energy level surfaces about the motion of a rigid body under external force.The proof was improved by the theory of differential topology and algebra topology.