P. Bernard, J.M. Roquejoffre Convergence to time-periodic solutions in Hamilton-Jacobi equations on the circle (232K, ps) ABSTRACT. The goal of this paper is to give a simple proof of the convergenceto time-periodic states of the viscosity solutions of time-periodic Hamilton-Jacobi equations on the circle with convex Hamiltonian. Note that the period of the limit solution may be greater than the period of the Hamiltonian.