We consider an exoplanetary system consisting of a star and two planets. The masses of the planets are significantly less than the mass of the star. The evolution of the orbital motion of exoplanets is studied within the framework of a double averaged unrestricted three-body problem. The main attention is paid to coplanar configurations, when the star and planets move in a certain plane that preserves a constant position. The possibility of reversing the orbital motion of the inner planet is noted.

Stellar bars are important internal drivers of the secular evolution of disk galaxies. Using a sample of nearby barred galaxies with weak and strong bars, we evaluate the correlations between star formation properties in different galactic structures and their associated bars, and try to interpret the complex process of bar-driven secular evolution. We find that weaker bars tend to associate with lower concentrical star formation activities, while stronger bars appear to have large scatter in the distribution of the global star formation activities. In general, the star formation activities in early- and late-type galaxies have different behavior, with similar star formation rate density distributions. In addition, there are only weak trends toward increased star formation activities in bulges and galaxies with stronger bars, which is consistent with previous works. Our results suggest that the different stages of the evolutionary sequence and many factors besides bars may contribute to the complexity of this process. Furthermore, significant correlations are found between the star formation activities in different galactic structures, in which barred galaxies with intense star formation in bulges tend to also have active star formation in their bars and disks. Most bulges have higher star formation densities than their associated bars and disks, indicating the presence of bar-driven evolution. Therefore, we derived a possible criterion (Figure 1) to quantify the different stages of a bar-driven evolutionary sequence. Future work is needed to improve on the uncertainties of this study.

Recent work on the dynamics of galaxy bulges has been dominated by two themes. (1) Bulges share the richness in kinematic structure that is currently being discovered in elliptical galaxies. This includes kinematic evidence for triaxiality and for accretion (counterrotating gas and stellar components). (2) The main subject of this paper is observational and theoretical evidence that some “bulges” are built secularly out of disk material. Many bulges show photometric and kinematic evidence for disklike dynamics. This includes (i) velocity dispersions σ much smaller than those predicted by the Faber-Jackson σ — M B correlation, (ii) rapid rotation V(r) that implies V/σ values well above the “oblate line” describing rotationally flattened, isotropic spheroids in the V/σ — ellipticity diagram, and (iii) spiral structure dominating the r 1/4 part of the galaxy. In these galaxies, the steep, r1/4-law central brightness profiles belong not to bulges but to disks. That is, some galaxy disks have central brightness profiles that are much steeper than the inward extrapolation of an exponential fit to the outer parts. These observations and n-body simulations of gas flow in nonaxisymmetric galaxies imply that high-central-concentration, flat components can be formed out of disk gas that is transported toward the center by bars and oval distortions. The n-body models suggest further that some “bulges” are built of disk stars heated in the axial direction by resonant scattering off of bars. These effects are signs that important secular evolution processes are at work in galaxy disks.