  We prove exponential convergence to time-periodic states of the solutions of
time-periodic Hamilton-Jacobi equations on the torus, assuming that the Aubry
set is the union of a finite number of hyperbolic periodic orbits of the the
Euler Lagrange flow. The period of limiting solutions is the least common
multiple of the periods of the orbits in the Aubry set. This extends a result
that we obtained in the autonomous case.
