  The GJ 436 system contains a transiting planet GJ 436 b which is a hot
analogue of Neptune on an eccentric orbit. Recently, two additional transiting
sub-Earth planets have been postulated in the literature. We observed three
transits of GJ 436 b over the course of 3 years using two-meter class
telescopes, each with a photometric precision better than one millimagnitude.
We studied system dynamics based on the existence of the additional planets. We
redetermined system parameters, which were in agreement with those found in the
literature. We refined the orbital period of GJ 436 b and found no evidence of
transit timing variations. The orbital motion of the GJ 436 c planet candidate
was found to be significantly affected by the planet b with variations in
transit times at a level of 20 minutes. As the orbital period of the GJ 436 d
planet candidate remains unknown, our numerical experiments rule out orbits in
low-order resonances with GJ 436 b. The GJ 436 system with the hot Neptune and
additional two Earth-like planets, if confirmed, would be an important
laboratory for studies of formation and evolution of planetary systems.
