  To date, 17 circumbinary planets have been discovered. In this paper, we
focus our attention on the stability of the Kepler circumbinary planetary
systems 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 of
such systems is an opportunity to test our understanding of planetary system
formation and evolution around binaries. The investigation is done by means of
numerical simulations. We perform numerical integrations of the full equations
of motion of each system with the aim of checking the stability of the
planetary orbit. The investigation of the stability of the above systems
consists of three numerical experiments. In the first one we perform a long
term (1Gyr) numerical integration of the nominal solution of the six Kepler
systems under investigation. In the second experiment, we look for the critical
semimajor axis of the six planetary orbits, and finally, in the third
experiment, we construct two dimensional stability maps on the
eccentricity-pericentre distance plane. Additionally, using numerical
integrations of the nominal solutions we checked if this solutions were close
to the exact resonance.
