轴对称星系型势场中的俘获和逃逸轨道
Trapped and escaping orbits in an axially symmetric galactic-type potential
摘要：
本文研究了与时间无关的轴对称星系型势中的轨道行为。这个动力学模型可以用来描述星系中心部分的运动，因为能量值大于逃逸能量。我们使用经典的截面曲面方法，以便可视化和解释动力系统相空间的结构。此外，李雅普诺夫特征指数（LCE），是用来在我们的银河系模型的轨道的混沌程度的估计。我们的数值计算表明，在这种星系型势中，存在两种轨道：（i）逃逸轨道和（ii）完全不逃逸的捕获轨道。此外，大量的动力系统的轨道，显示混沌运动。在混沌轨道中，有快速逃逸的轨道，也有在很长一段时间内被困的轨道。当测试粒子的能量值稍微超过逃逸能量时，捕获的规则轨道的数量随着角动量值的增加而增加。因此，在相平面中观察到的混沌区域的范围随着能量值的增加而减小。此外，我们计算的逃逸周期的混沌轨道的平均值，我们试图将它与能量的值，也与z分量的轨道的最大值。此外，我们发现，对应于每个混沌区域的LCE的值，对于不同的能量值，随着能量值的增加呈指数增长。一些理论参数，以支持数值得到的结果。
英文摘要：
In the present article, we investigate the behavior of orbits in a time independent axially symmetric galactic type potential. This dynamical model can be considered to describe the motion in the central parts of a galaxy, for values of energies larger than the energy of escape. We use the classical method of the surface of section, in order to visualize and interpret the structure of the phase space of the dynamical system. Moreover, the Lyapunov Characteristic Exponent (LCE), is used in order to make an estimation of the degree of the chaoticity of the orbits in our galactic model. Our numerical calculations suggest that in this galactic type potential, there are two kinds of orbits: (i) escaping orbits and (ii) trapped orbits which do not escape at all. Furthermore, a large number of orbits of the dynamical system, display chaotic motion. Among the chaotic orbits, there are orbits that escape fast and also orbits that remain trapped for vast time intervals. When the value of the test particle's energy exceeds slightly the energy of escape, the amount of the trapped regular orbits increases, as the the value of the angular momentum increases. Therefore, the extent of the chaotic regions observed in the phase plane decreases as the value of the energy increases. Moreover, we calculate the average value of the escape period of the chaotic orbits and we try to correlate it with the value of the energy and also with the maximum value of the z component of the orbits. In addition, we find that the value of the LCE corresponding to each chaotic region, for different values of the energy, increases exponentially as the value of the energy increases. Some theoretical arguments in order to support the numerically obtained outcomes are presented.
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