  We perform numerical simulations of the TRAPPIST-1 system of seven exoplanets
orbiting a nearby M dwarf, starting with a previously suggested stable
configuration. The long-term stability of this configuration is confirmed, but
the motion of planets is found to be chaotic. The eccentricity values are found
to vary within finite ranges. The rates of tidal dissipation and tidal
evolution of orbits are estimated, assuming an Earth-like rheology for the
planets. We find that under this assumption the planets b, d, e were captured
in the 3:2 or higher spin-orbit resonances during the initial spin-down but
slipped further down into the 1:1 resonance. Dependent on its rheology, the
innermost planet b may be captured in a stable pseudosynchronous rotation.
Non-synchronous rotation ensures higher levels of tidal dissipation and
internal heating. The positive feedback between the viscosity and the
dissipation rate -- and the ensuing runaway heating -- are terminated by a few
self-regulation processes. When the temperature is high and the viscosity is
low enough, the planet spontaneously leaves the 3:2 resonance. Further heating
is stopped either by passing the peak dissipation or by the emergence of
partial melt in the mantle. In the post-solidus state, the tidal dissipation is
limited to the levels supported by the heat transfer efficiency. The tides on
the host star are unlikely to have had a significant dynamical impact. The
tides on the synchronized inner planets tend to reduce these planets' orbital
eccentricity, possibly contributing thereby to the system's stability.
