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To date, 17 circumbinary planets have been discovered. In this paper, wefocus our attention on the stability of the Kepler circumbinary planetarysystems with only one planet, i.e. Kepler-16, Kepler-34, Kepler-35, Kepler-38,Kepler-64 and Kepler-413. In addition to their intrinsic interest, the study ofsuch systems is an opportunity to test our understanding of planetary systemformation and evolution around binaries. The investigation is done by means ofnumerical simulations. We perform numerical integrations of the full equationsof motion of each system with the aim of checking the stability of theplanetary orbit. The investigation of the stability of the above systemsconsists of three numerical experiments. In the first one we perform a longterm (1Gyr) numerical integration of the nominal solution of the six Keplersystems under investigation. In the second experiment, we look for the criticalsemimajor axis of the six planetary orbits, and finally, in the thirdexperiment, we construct two dimensional stability maps on theeccentricity-pericentre distance plane. Additionally, using numericalintegrations of the nominal solutions we checked if this solutions were closeto the exact resonance.

A dynamical stability study of Kepler Circumbinary Planetary systems with one planet