GALI方法在非线性系统局部化动力学中的应用
Application of the GALI Method to Localization Dynamics in Nonlinear Systems
摘要：
研究了$N$自由度Hamilton系统和$N$耦合辛映射中拟周期振荡的局部化现象和稳定性。特别是，我们研究了一个例子的参数驱动的哈密顿晶格只有四次耦合项和一个系统的$N$耦合的标准映射。我们探索他们的动力学使用的广义排列指数（GALI），这构成了一个最近开发的数值方法检测混沌轨道在许多方面，估计准周期环面的维数和预测慢扩散的方式，是更快，更可靠的比许多其他方法已知的日期。
英文摘要：
We investigate localization phenomena and stability properties of quasiperiodic oscillations in $N$ degree of freedom Hamiltonian systems and $N$ coupled symplectic maps. In particular, we study an example of a parametrically driven Hamiltonian lattice with only quartic coupling terms and a system of $N$ coupled standard maps. We explore their dynamics using the Generalized Alignment Index (GALI), which constitutes a recently developed numerical method for detecting chaotic orbits in many dimensions, estimating the dimensionality of quasiperiodic tori and predicting slow diffusion in a way that is faster and more reliable than many other approaches known to date.
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