12-70 Xifeng Su, Rafael de la Llave
KAM theory for quasi-periodic equilibria in 1D quasiperiodic media--II: long-range interactions (256K, pdf) Jun 18, 12
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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.

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