扁圆卫星转动模型的分叉图和广义分叉图
Bifurcation Diagrams and Generalized Bifurcation Diagrams for a rotational model of an oblate satellite
摘要：
本文给出了一个扁圆卫星转动模型的分支图和广义分支图。特别注意的是参数值描述土星的卫星之一，土星。对于不同的扁率的最大李雅普诺夫特征指数（LCE）绘制。在初始条件以及在混合参数初始条件空间中的最大LCE表现出分形结构，为分形维数计算。它是由分岔图的结果，其中大多数的参数值预选的初始条件导致混沌旋转。第一重现时间（FRT）图解释了混沌的产生和分岔图中准周期窗口的存在。
英文摘要：
This paper presents bifurcation and generalized bifurcation diagrams for a rotational model of an oblate satellite. Special attention is paid to parameter values describing one of Saturn's moons, Hyperion. For various oblateness the largest Lyapunov Characteristic Exponent (LCE) is plotted. The largest LCE in the initial condition as well as in the mixed parameter-initial condition space exhibits a fractal structure, for which the fractal dimension was calculated. It results from the bifurcation diagrams of which most of the parameter values for preselected initial conditions lead to chaotic rotation. The First Recurrence Time (FRT) diagram provides an explanation of the birth of chaos and the existence of quasi-periodic windows occuring in the bifurcation diagrams.
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