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 three 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.