|Location:||MSRI: Simons Auditorium|
We consider a quasi-periodic version of the well-known Frenkel-Kontorova
model and looking for quasi-periodic equilibria with a frequency that resonates with the
frequencies of the medium. We show that there are always perturbative expansions and
prove a KAM theorem in a-posteriori form. We show that if there is an approximate
solution of the equilibrium equation satisfying non-degeneracy conditions, we can adjust
one parameter and obtain a true solution which is close to the approximate solution. The
proof is based on an iterative method of the KAM type.