论文标题
关于多维哈密顿系统中常规运动的广义比对指数（GALI）方法的行为
On the behavior of the Generalized Alignment Index (GALI) method for regular motion in multidimensional Hamiltonian systems
论文作者
论文摘要
我们研究了多维汉密尔顿系统的常规轨道的订单$ k $（gali $ _k $）的广义对齐指数的行为。 gali $ _k $是一个有效的混乱指标，当$ 2 \ leq k \ leq n $时渐近地达到正常运动的正值，其中$ n $是运动发生的圆环的维度。通过在附近考虑几个典型的简单，稳定的周期性轨道，用于Fermi-pasta-ulam-tsingou（fput）$β$模型，用于系统的自由度的各种值，我们表明，当指数$ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k nertive y noce y note y note y nock y nock y noce y note n oferbit sight nock y nocials Orbit的序列时，范围均可降低。消失，当考虑的常规轨道远离周期性的固定能量以获得固定能量时，它们会增加。此外，进行广泛的数值模拟我们表明，该指数的行为不取决于选择其评估所需的初始偏差向量。
We investigate the behavior of the Generalized Alignment Index of order $k$ (GALI$_k$) for regular orbits of multidimensional Hamiltonian systems. The GALI$_k$ is an efficient chaos indicator, which asymptotically attains positive values for regular motion when $2\leq k \leq N$, with $N$ being the dimension of the torus on which the motion occurs. By considering several regular orbits in the neighborhood of two typical simple, stable periodic orbits of the Fermi-Pasta-Ulam-Tsingou (FPUT) $β$ model for various values of the system's degrees of freedom, we show that the asymptotic GALI$_k$ values decrease when the index's order $k$ increases and when the orbit's energy approaches the periodic orbit's destabilization energy where the stability island vanishes, while they increase when the considered regular orbit moves further away from the periodic one for a fixed energy. In addition, performing extensive numerical simulations we show that the index's behavior does not depend on the choice of the initial deviation vectors needed for its evaluation.
