The Homology Classes of Large-Scale Periodic Orbits on Nonlinear Space
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摘要: 非线性力学系统的大范围周期轨道可以代表等能曲面上的同调类,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及哈密顿函数的大尺度性质决定。本文用后两类性质估算了等能曲面的第1同调群的秩。Abstract: The large-scale periodic orbits of a nonlinear mechanics system can represent the homology classes, which are generally non-trivial, of the energy level surface and the topology properties of an energy level surface are determined by the that of the phase space and the large-scale properties of the Hamiltonian. These properties are used for estimate of the rank of first homology group of energy level surfaces in the paper.
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Key words:
- large-scale periodic motion /
- homology classes /
- Morsc inequalities
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[1] Edwin H.Spanier,Algebraic Topology,Springer-Verlag(1966). [2] R.Bott,Lectures on Morse theory,old and new,Bull.Am er.Math.Soc.(New Series),7(2) (1982),331)358. [3] Morris W.Hirsch,Differential Topology,Springer-Verlag(1976). [4] Ralph Abraham and Jerrold E.Marsden,Foundations of Mechanics,Second Edition,The Benjamin/Cummings Publishing Company,Inc.(1978). [5] V.I.Arnold,Mathematical Methods of Classical Mechanics,Springer-Verlag(1978). -
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