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Discoveries of exoplanets orbiting evolved stars motivate critical examinations of the dynamics of N -body systems with mass loss. Multi-planet evolved systems are particularly complex because of the mutual interactions between the planets. Here, we study the underlying dynamical mechanisms which can incite planetary escape in two-planet post-main sequence systems. Stellar mass loss alone is unlikely to be rapid and high enough to eject planets at typically-observed separations. However, the combination of mass loss and planetplanet interactions can prompt a shift from stable to chaotic regions of phase space. Consequently, when mass loss ceases, the unstable configuration may cause escape. By assuming a constant stellar mass loss rate, we utilize maps of dynamical stability to illustrate the distribution of regular and chaotic trajectories in phase space. We show that chaos can drive the planets to undergo close encounters, leading to the ejection of one planet. Stellar mass loss can trigger the transition of a planetary system from a stable to chaotic configuration, subsequently causing escape. We find that mass loss non-adiabatically affects planet-planet interaction for the most massive progenitor stars which avoid the supernova stage. For these cases, we present specific examples of planetary escape.

The birth and death of planets may be affected by mass outflows from their parent stars during the T-Tauri or post-main-sequence phases of stellar evolution. These outflows are often modelled to be isotropic, but this assumption is not realistic for fast rotators, bipolar jets and supernovae. Here we derive the general equations of motion for the time evolution of a single planet, brown dwarf, comet or asteroid perturbed by anisotropic mass loss in terms of a complete set of planetary orbital elements, the ejecta velocity, and the parent star's co-latitude and longitude. We restrict our application of these equations to 1) rapidly rotating giant stars, and 2) arbitrarily-directed jet outflows. We conclude that the isotropic mass-loss assumption can safely be used to model planetary motion during giant branch phases of stellar evolution within distances of hundreds of au. In fact, latitudinal mass loss variations anisotropically affect planetary motion only if the mass loss is asymmetric about the stellar equator. Also, we demonstrate how constant-velocity, asymmetric bipolar outflows in young systems incite orbital inclination changes. Consequently, this phenomenon readily tilts exoplanetary orbits external to a nascent disc on the order of degrees.

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We present a global view of the resonant structure of the phase space of a planetary system with two planets, moving in the same plane, as obtained from the set of the families of periodic orbits. An important tool to understand the topology of the phase space is to determine the position and the stability character of the families of periodic orbits. The region of the phase space close to a stable periodic orbit corresponds to stable, quasi periodic librations. In these regions it is possible for an extrasolar planetary system to exist, or to be trapped following a migration process due to dissipative forces. The mean motion resonances are associated with periodic orbits in a rotating frame, which means that the relative configuration is repeated in space. We start the study with the family of symmetric periodic orbits with nearly circular orbits of the two planets. Along this family the ratio of the periods of the two planets varies, and passes through rational values, which correspond to resonances. At these resonant points we have bifurcations of families of resonant elliptic periodic orbits. There are three topologically different resonances: (1) the resonances (n + 1):n, (2:1, 3:2, …), (2) the resonances (2n + 1):(2n − 1), (3:1, 5:3, …) and (3) all other resonances. The topology at each one of the above three types of resonances is studied, for different values of the sum and of the ratio of the planetary masses. Both symmetric and asymmetric resonant elliptic periodic orbits exist. In general, the symmetric elliptic families bifurcate from the circular family, and the asymmetric elliptic families bifurcate from the symmetric elliptic families. The results are compared with the position of some observed extrasolar planetary systems. In some cases (e.g., Gliese 876) the observed system lies, with a very good accuracy, on the stable part of a family of resonant periodic orbits.

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