论文标题
在同型和杂斜轨道附近的单度哈密顿系统的时间周期性扰动的不整合性
Nonintegrability of time-periodic perturbations of single-degree-of-freedom Hamiltonian systems near homo- and heteroclinic orbits
论文作者
论文摘要
我们考虑了哈密顿系统的单度自由度的时间扰动，并研究了由于Morales-Ramis理论的Ayoul和Zung，使用广义版本使用广义版本在Bogoyavlenskij sense中进行真实的非整合性。假定扰动术语在时间上具有有限的傅立叶序列，并且被扰动的系统被重写为具有小参数作为状态变量的较高维度自主系统。我们的结果不仅是同质轨道上的先前结果扩展到异斜轨道的结果，而且对于同质轨道轨道的情况而言，它们比它们提供了更强的结论。我们说明了两个定期强迫振荡振荡器和一个定期强迫二维系统的理论。
We consider time-periodic perturbations of single-degree-of-freedom Hamiltonian systems and study their real-meromorphic nonintegrability in the Bogoyavlenskij sense using a generalized version due to Ayoul and Zung of the Morales-Ramis theory. The perturbation terms are assumed to have finite Fourier series in time, and the perturbed systems are rewritten as higher-dimensional autonomous systems having the small parameter as a state variable.We show that if the Melnikov functions are not constant, then the autonomous systems are not real-meromorphically integrable near homo- and heteroclinic orbits. Our result is not just an extension of previous results for homocliic orbits to heteroclinic orbits and provides a stronger conclusion than them for the case of homoclinic orbits. We illustrate the theory for two periodically forced Duffing oscillators and a periodically forced two-dimensional system.
