一维非自治哈密顿系统的周期轨道
Periodic orbits of a one dimensional non autonomous Hamiltonian system
摘要：
本文研究了x + V '_x（t，x）= 0的周期轨道的性质，其中x为\in S1，V（t，x）为T0周期势.称之为ρ \in（1/T0）Q，S 1中轨道的缠绕频率，我们证明了存在无穷多个周期解。利用莫尔斯理论给出了周期和ρ都给定的周期轨道个数的一个下界.
英文摘要：
In this paper we study the properties of the periodic orbits of x + V'_x(t, x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called ρ \in (1/T0)Q the frequency of windings of an orbit in S1 we show that exists an infinite number of periodic solutions with a given ρ. We give a lower bound on the number of periodic orbits with a given period and ρ by means of the Morse theory.
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