Extra-Solar planetary system

For an updated list of the known extra-solar planetary systems see table at http //obswww.unige.ch/Exoplanets... 

Abstract The periodic orbits play an important role in the study of the stability of a dynamical system. The methods of study of the stability of a periodic orbit are presented both in the general case and for Hamiltonian systems. The Poincare map on a surface of section is presented as a powerful tool in the study of a dynamical system, especially for two or three degrees of freedom. Special attention is given to nearly integrable dynamical systems, because our solar system and the extra solar planetary systems are considered as perturbed Keplerian systems. The continuation of the families of periodic orbits from the unperturbed, integrable, system to the perturbed, nearly integrable system, is studied. 

REGULAR MOTIONS IN EXTRA-SOLAR PLANETARY SYSTEMS... 

Regular motions in extra-solar planetary systems... 

The contents of this paper include, with variable emphasis, the topics of a series of lectures whose main title was Routes to Order Capture into resonance . This was indeed the subject of the last section above. The study of this subject has, however, shown that - unlike the restricted three-body problem - capture into resonance drives the system immediately to stationary solutions known as Apsidal corotations . The whole theory of these solutions was also included in the paper from the beginning - that is, from the formulation of the Hamiltonian equations of the planetary motions and the expansion of the disturbing function in the high-eccentricity planetary three-body problem. The secular theory of non-resonant systems was also given. Motions with aligned or anti-aligned periapses, resonant or not, resulting from non-conservative processes (tidal interactions with the disc) in the early phases of the life of the system, seem to be frequent in extra-solar planetary systems. 

The discovery of the first extra-solar planet in orbit around a main-sequence star was announced in 1995. Since then, the number of known Extra-Solar Planets has not ceased to grow. As observations accumulate, planetary systems with 2 and 3 planets are being discovered. More than... 

Mayor, M., Udry, S., Lovis, C., Repe, R, Queloz, D., Benz, W, Bertaux, J.-L., Bouchy, R, Mordasini, C., Segransan, D. The HARRS search for southern extra-solar planets. XIII. A planetary system with 3 super-Earths (4.2,6.9, and 9.2 M.). Astron. Astrophys. 493,639-644 (2009)... 

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