论文标题
基于轨道幅度的分离和混乱的海洋检测
Detection of separatrices and chaotic seas based on orbit amplitudes
论文作者
论文摘要
最大偏心法（MEM）是分析行星系统及其稳定性的标准工具。该方法等于在初始条件的采样域上估计轨道的最大轨道拉伸。目前的纸张利用MEM引入了分离和混乱的尖锐探测器。在引入了几乎可动的动作角度哈密顿量（即直径）的MEM类似物之后，我们使用具有多共振模式和交界处的低维动力系统，支持混乱的运动，以识别直径指标的驱动因素。一旦对此表示感谢，我们就会提出一个基于第二个衍生的索引，以测量该应用程序的规律性。该数量变为一种敏感且健壮的指标，可检测分离，谐振网和混乱的海洋。我们讨论了该框架在$ n $ body模拟的上下文中针对受平均动作共振影响的行星案例的实际应用，并演示了该索引区分相位空间的分钟结构的能力，否则未通过原始mem进行了否则。
The Maximum Eccentricity Method (MEM) is a standard tool for the analysis of planetary systems and their stability. The method amounts to estimating the maximal stretch of orbits over sampled domains of initial conditions. The present paper leverages on the MEM to introduce a sharp detector of separatrices and chaotic seas. After introducing the MEM analogue for nearly-integrable action-angle Hamiltonians, i.e., diameters, we use low-dimensional dynamical systems with multi-resonant modes and junctions, supporting chaotic motions, to recognise the drivers of the diameter metric. Once this is appreciated, we present a second-derivative based index measuring the regularity of this application. This quantity turns to be a sensitive and robust indicator to detect separatrices, resonant webs and chaotic seas. We discuss practical applications of this framework in the context of $N$-body simulations for the planetary case affected by mean-motion resonances, and demonstrate the ability of the index to distinguish minute structures of the phase space, otherwise undetected with the original MEM.
