  When exploring the stability of multiplanet systems in binaries, two
parameters are normally exploited: the critical semimajor axis ac computed by
Holman and Wiegert (1999) within which planets are stable against the binary
perturbations, and the Hill stability limit Delta determining the minimum
separation beyond which two planets will avoid mutual close encounters. Our aim
is to test whether these two parameters can be safely applied in multiplanet
systems in binaries or if their predictions fail for particular binary orbital
configurations. We have used the frequency map analysis (FMA) to measure the
diffusion of orbits in the phase space as an indicator of chaotic behaviour.
First we revisited the reliability of the empirical formula computing ac in the
case of single planets in binaries and we find that, in some cases, it
underestimates by 10-20% the real outer limit of stability. For two planet
systems, the value of Delta is close to that computed for planets around single
stars, but the level of chaoticity close to it substantially increases for
smaller semimajor axes and higher eccentricities of the binary orbit. In these
configurations ac also begins to be unreliable and non linear secular
resonances with the stellar companion lead to chaotic behaviour well within ac,
even for single planet systems. For two planet systems, the superposition of
mean motion resonances, either mutual or with the binary companion, and non
linear secular resonances may lead to chaotic behaviour in all cases. We have
developed a parametric semiempirical formula determining the minimum value of
the binary semimajor axis, for a given eccentricity of the binary orbit, below
which stable two planet systems cannot exist.
