标题： 哈密顿棒状星系模型中的复杂统计 显示英文标题

标题： Complex statistics in Hamiltonian barred galaxy models

摘要： 我们使用轨道坐标在约一个哈勃时间的时间间隔内的和的概率密度函数（pdfs），以区分棒旋星系模型中的弱混沌轨道和强混沌轨道。 我们发现，在弱混沌的情况下，准稳态出现，其pdfs可以很好地用$q$-高斯函数（带有$1<q<3$）近似，而强混沌则由迅速趋向高斯分布的pdfs标识（$q=1$）。 弱混沌轨道的典型例子是那些“粘附”在有序运动岛屿上的轨道。 由于它们能够在相对较长时间尺度上支持星系结构，近年来在旋转星系模型中对它们的存在进行了深入研究。 在本文中，我们在2自由度和3自由度棒旋星系模型的具体轨道上展示了所提出的统计方法可以准确且高效地区分弱混沌和强混沌运动，尤其是在李雅普诺夫指数和其他局部动力学指标似乎不明确的情况下。 显示英文摘要

摘要： We use probability density functions (pdfs) of sums of orbit coordinates, over time intervals of the order of one Hubble time, to distinguish weakly from strongly chaotic orbits in a barred galaxy model. We find that, in the weakly chaotic case, quasi-stationary states arise, whose pdfs are well approximated by $q$-Gaussian functions (with $1<q<3$), while strong chaos is identified by pdfs which quickly tend to Gaussians ($q=1$). Typical examples of weakly chaotic orbits are those that "stick" to islands of ordered motion. Their presence in rotating galaxy models has been investigated thoroughly in recent years due of their ability to support galaxy structures for relatively long time scales. In this paper, we demonstrate, on specific orbits of 2 and 3 degree of freedom barred galaxy models, that the proposed statistical approach can distinguish weakly from strongly chaotic motion accurately and efficiently, especially in cases where Lyapunov exponents and other local dynamic indicators appear to be inconclusive.