论文标题
关于堕落的周期性轨道通过正常形式的延续：较低的谐振托里
On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori
论文作者
论文摘要
我们认为，在几乎可集成的哈密顿系统中，周期性轨道延续的经典问题是在不变的下维谐振托里（Tori）中损坏的问题。特别是，我们将以前的结果（在CNSN，61：198-224，2018）扩展到全尺寸谐振托里到较低的结果。我们开发了一种建设性的正常形式方案，该方案允许识别和近似谐振圆环破裂后继续存在的周期轨道。我们算法的特定特征是处理堕落的周期性轨道。此外，在近似周期轨道的适当假设下，我们获得了有关周期性轨道可行的延续可行轨道线性稳定性的信息。还提供了一个涉及几个自由度的教学示例，但还提供了与DNLS局部离散孤子的经典主题相关的。
We consider the classical problem of the continuation of periodic orbits surviving to the breaking of invariant lower dimensional resonant tori in nearly integrable Hamiltonian systems. In particular we extend our previous results (presented in CNSNS, 61:198-224, 2018) for full dimensional resonant tori to lower dimensional ones. We develop a constructive normal form scheme that allows to identify and approximate the periodic orbits which continue to exist after the breaking of the resonant torus. A specific feature of our algorithm consists in the possibility of dealing with degenerate periodic orbits. Besides, under suitable hypothesis on the spectrum of the approximate periodic orbit, we obtain information on the linear stability of the periodic orbits feasible of continuation. A pedagogical example involving few degrees of freedom, but connected to the classical topic of discrete solitons in dNLS-lattices, is also provided.
