  We establish a connection between the Aubry-Mather theory of invariant sets
of a 1D dynamical system described by a Lagrangian with potential periodic in
space and time, on the one hand, and idempotent spectral theory of the Bellman
operator of the corresponding optimization problem, on the other hand. This
connection is applied to obtain a uniqueness result for an eigenfunction of the
Bellman operator in the case of irrational rotation number.
