Persistence of Invariant Tori in Integrable Hamiltonian Systems Under Almost Periodic Perturbations
Persistence of Invariant Tori in Integrable Hamiltonian Systems Under Almost Periodic Perturbations
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DOI：
10.1007/s00332-018-9467-9
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发表时间：
2018-06
影响因子：
3
通讯作者：
Peng-Ru Huang;Xiong Li
中科院分区：
文献类型：
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作者：
Peng-Ru Huang;Xiong Li
本文研究了近可积Hamilton系统H=h（y）+f（x，y，t），其中D是开有界区域，f（x，y，t）是真实的解析概周期函数，其频率为int的不变环面的存在性.作为应用，我们将证明具有几乎周期依赖于时间的超二次位势的二阶微分方程的概周期解的存在性和所有解的有界性。
In this paper, we are concerned with the existence of invariant tori in nearly integrable Hamiltonian systems $$\begin{aligned} H=h(y)+f(x,y,t), \end{aligned}$$wherewithDbeing an open bounded domain,,f(x,y,t) is a real analytic almost periodic function intwith the frequency. As an application, we will prove the existence of almost periodic solutions and the boundedness of all solutions for the second-order differential equations with superquadratic potentials depending almost periodically on time.