96-253 H. Koch, R. de la Llave, C. Radin
Aubry-Mather theory for functions on lattices. (66K, Plain TeX) Jun 10, 96
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Abstract. We generalize the Aubry-Mather theorem on the existence of quasi-periodic solutions of one dimensional difference equations to situations in which the independent variable ranges over more complicated lattices. This is a natural generalization of Frenkel-Kontorovna models to physical situations in a higher dimensional space. We also consider generalizations in which the interactions among the particles are not just nearest neighbor, and indeed do not have finite range.

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