边缘冲浪：类木行星系统中的混沌与近可积性
Surfing on the Edge: Chaos vs. Near-Integrability in the System of Jovian Planets
摘要：
我们证明了木星行星系统（太阳+木星+土星+天王星+海王星），集成了2亿年，作为一个孤立的5体系统，使用许多套初始条件都在其目前已知的位置的不确定性范围内，可以显示混乱和近可积性。结论是一致的，在四个不同的积分器，包括几个比较积分利用四倍精度。我们证明，智慧霍尔曼辛映射使用简单的辛校正器实现在水星6.2（钱伯斯1999年）给出了一个可靠的表征混沌的存在，只有一个特定的初始条件下的时间步长小于约10天，对应于约400步每轨道。我们还将标准的DE 405初始条件积分到5 Gy，并表明它有一个200- 400 My的李雅普诺夫时间，打开了精确预测5 Gy木星行星位置的遥远的可能性。
英文摘要：
We demonstrate that the system of Jovian planets (Sun+Jupiter+Saturn+Uranus+Neptune), integrated for 200 million years as an isolated 5-body system using many sets of initial conditions all within the uncertainty bounds of their currently known positions, can display both chaos and near-integrability. The conclusion is consistent across four different integrators, including several comparisons against integrations utilizing quadruple precision. We demonstrate that the Wisdom-Holman symplectic map using simple symplectic correctors as implemented in Mercury 6.2 (Chambers 1999) gives a reliable characterization of the existence of chaos for a particular initial condition only with timesteps less than about 10 days, corresponding to about 400 steps per orbit. We also integrate the canonical DE405 initial condition out to 5 Gy, and show that it has a Lyapunov Time of 200--400 My, opening the remote possibility of accurate prediction of the Jovian planetary positions for 5 Gy.
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