  Let $M$ be a closed and connected manifold, $H:T^*M\times \mathbb{R} /
\mathbb{Z} \to \mathbb{R}$ a Tonelli $1$-periodic Hamiltonian and $\mathcal{L}
\subset T^*M$ a Lagrangian submanifold Hamiltonianly isotopic to the zero
section. We prove that if $\mathcal{L}$ is invariant by the time-one map of
$H$, then $\mathcal{L}$ is a graph over $M$. An interesting consequence in the
autonomous case is that in this case, $\mathcal{L}$ is invariant by all the
time $t$ maps of the Hamiltonian flow of $H$.

Dynamical Systems