标题： 高阶行星系统中内侧探测粒子的长期共振结构 显示英文标题

标题： Structures of secular resonances for inner test particles in hierarchical planetary systems

摘要： 在本研究中，通过采用非摄动方法，在三级近似下研究了内侧测试粒子的长期共振动力学。实际上，通过识别稳定的周期轨道族，生成了主要长期共振的网络，并通过分析庞加莱截面获得了相关的稳定摆动区域。通过取不同的因子值$\epsilon$（$\epsilon$衡量三级项的贡献），评估了三级项对动力学结构的影响。在$\epsilon = 0$（无三级项贡献）的条件下，动力学模型完全可积，相空间中仅出现科齐共振。当因子$\epsilon$不为零时，由于各种长期共振的出现，相空间中的动力学结构变得复杂。数值结果进一步表明：(a) 摆动中心和稳定摆动区域的分布随着$\epsilon$的不同值而保持定性相似；(b) 由于低偏心率区域内的混沌运动，科齐共振消失；(c) 低偏心率区域内出现的混沌区域随因子$\epsilon$的增加而增大。长期共振是许多重要动力学现象（如混沌、轨道对齐和轨道翻转）的根源，因此本工作的结果可能有助于理解等级行星系统中那些高偏心率和/或高倾角天体的长期动力学。 显示英文摘要

摘要： In this study, dynamics of secular resonances for inner test particles are investigated under the octupole-level approximation by taking non-perturbative approaches. In practice, webs of the major secular resonances are produced by identifying families of stable periodic orbits and the associated stable libration zones are obtained by analysing Poincar\'e surfaces of section. By taking different values of the factor $\epsilon$ ($\epsilon$ measures the contribution of octupole terms), the influences of the octupole-order terms upon the dynamical structures are evaluated. Under the condition of $\epsilon = 0$ (no octupole-order contribution), the dynamical model is totally integrable and there is only Kozai resonance arising in the phase space. When the factor $\epsilon$ is different from zero, the dynamical structure in the phase space becomes complicated due to varieties of secular resonances appearing. Numerical results further indicate that (a) distributions of libration centres and stable libration zones remain qualitatively similar with different values of $\epsilon$, (b) Kozai resonance disappears due to the chaotic motion in the low-eccentricity region, and (c) the chaotic area arising in the low-eccentricity region increases with the factor $\epsilon$. Secular resonances are the source of many important dynamical phenomena, such as chaos, orbit alignment and orbit flipping, and thus the results presented in this work could be useful to understand the secular dynamics for those high-eccentricity and/or high-inclination objects in hierarchical planetary systems.