Xifeng Su, Rafael de la Llave
KAM theory for quasi-periodic equilibria in 1D quasiperiodic media--II: long-range interactions
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ABSTRACT.  We consider Frenkel-Kontorova models corresponding to 1 dimensional 
quasi-crystal with non-nearest neighbor interactions. We formulate and prove a 
KAM type theorem 
which establishes the existence of quasi-periodic solutions. 
The interactions we consider do not need to be of finite range but 
do have to decay sufficiently fast with respect to the distance of 
the position of the atoms. The KAM theorem we present has an 
a-posteriori format. We do not need to assume that the system is 
close to integrable. We just assume that there is an approximate 
solution for the functional equation which satisfies some 
non-degeneracy conditions.