Aubry-Mather theory for functions on lattices | Zendy

Hans P. Koch | Zendy; Rafael de la Llave | Zendy; Charles Radin | Zendy

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Aubry-Mather theory for functions on lattices

Author(s) -

Hans P. Koch,

Rafael de la Llave,

Charles Radin

Publication year - 1997

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.1997.3.135

Subject(s) - generalization , space (punctuation) , mathematics , variable (mathematics) , pure mathematics , range (aeronautics) , statistical physics , physics , mathematical analysis , computer science , materials science , composite material , operating system

. We generalize the Aubry-Mather theorem on the existence of quasiperiodicsolutions of one dimensional difference equations to situations in which theindependent variable ranges over more complicated lattices. This is a natural generalizationof Frenkel-Kontorovna models to physical situations in a higher dimensionalspace. We also consider generalizations in which the interactions among the particlesare not just nearest neighbor, and indeed do not have finite range.(1)This preprint is...

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