The Secular Evolution and Dynamical Architecture of the Neptunian   Triplet Planetary System HD 69830
  We perform numerical simulations to study the secular orbital evolution and dynamical structure in the HD 69830 system with the best-fit orbital solutions by Lovis and coworkers (2006). In the simulations, we show that the triplet Neptunian system can be stable at least for 2 Gyr and the stability would not be greatly influenced even if we vary the planetary masses. In addition, we employ the Laplace-Lagrange secular theory to investigate the long-term behaviors of the system, and the outcomes demonstrate that this theory can well describe the secular orbital evolution for all planets, where the secular periods and amplitudes in the eccentricities well agrees with those of the direct numerical integrations. We first reveal that the secular periods of the eccentricity $e_{1}$ and $e_{2}$ are identical about 8,300 yr. Moreover, we explore the planetary configuration of three Neptune-mass companions with one massive terrestrial planet in 0.07 AU $\leq a \leq 1.20$ AU, to examine the asteroid structure in this system. We underline that there are stable zones at least $10^{5}$ yr for low-mass terrestrial planets locating between 0.3 and 0.5 AU, and 0.8 and 1.2 AU with final low eccentricities. Still, we also find that the secular resonance $\nu_{1}$ and $\nu_{2}$ of two inner planets can excite the eccentricities of the terrestrial bodies, and the accumulation or depletion of the asteroid belt are also shaped by orbital resonances of the outer planets, i.e., 5:2 and 1:2 MMRs with Planet D... (abridged) 
Ji Jianghui (1,2,3), H. Kinoshita (4), Liu Lin (5), Li Guangyu (1,2)   ((1)Purple Mountain Observatory, CAS (2)NAOC, (3)DTM,...