混沌旋臂的解析形式
Analytical forms of chaotic spiral arms
摘要：
我们发展了一个星系中混沌旋臂的分析理论。这是基于不稳定周期轨道周围不变流形的莫泽理论。我们将这一理论应用于混沌旋臂，即从附近的拉格朗日点L1和L2在酒吧的结束在棒旋星系。表示从拉格朗日点L1、L2开始的不变流形或围绕L1和L2的不稳定周期轨道的级数在位形空间中产生螺旋图案。这些级数收敛于一个围绕每个拉格朗日点的域中，称为“莫泽域”，代表构成混沌旋臂的轨道。事实上，这些轨道不仅沿着不变流形，而且在不变流形周围的区域中。我们进一步表明，轨道开始以外的莫泽域，但接近它收敛到边界的莫泽域，它作为一个吸引子。这些轨道在逃逸到无穷远之前会在旋臂附近停留很长一段时间。
英文摘要：
We develop an analytical theory of chaotic spiral arms in galaxies. This is based on the Moser theory of invariant manifolds around unstable periodic orbits. We apply this theory to the chaotic spiral arms, that start from the neighborhood of the Lagrangian points L1 and L2 at the end of the bar in a barred-spiral galaxy. The series representing the invariant manifolds starting at the Lagrangian points L1, L2, or unstable periodic orbits around L1 and L2, yield spiral patterns in the configuration space. These series converge in a domain around every Lagrangian point, called "Moser domain" and represent the orbits that constitute the chaotic spiral arms. In fact, these orbits are not only along the invariant manifolds, but also in a domain surrounding the invariant manifolds. We show further that orbits starting outside the Moser domain but close to it converge to the boundary of the Moser domain, which acts as an attractor. These orbits stay for a long time close to the spiral arms before escaping to infinity.
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