  Transit timing variations (TTVs) are useful to constrain the existence of
perturbing planets, especially in resonant systems where the variations are
strongly enhanced. Here we focus on Laplace-resonant three-planet systems, and
assume the inner planet transits the star. A dynamical study is performed for
different masses of the three bodies, with a special attention to terrestrial
planets. We consider a maximal time-span of ~ 100 years and discuss the shape
of the inner planet TTVs curve. Using frequency analysis, we highlight the
three periods related to the evolution of the system: two periods associated
with the Laplace-resonant angle and the third one with the precession of the
pericenters. These three periods are clearly detected in the TTVs of an inner
giant planet perturbed by two terrestrial companions. Only two periods are
detected for a Jupiter-Jupiter-Earth configuration (the ones associated with
the giant interactions) or for three terrestrial planets (the Laplace periods).
However, the latter system can be constrained from the inner planet TTVs. We
finally remark that the TTVs of resonant three or two Jupiter systems mix up,
when the period of the Laplace resonant angle matches the pericenter precession
of the two-body configuration. This study highlights the importance of TTVs
long-term observational programs for the detection of multiple-planet resonant
systems.
