 1270 Xifeng Su, Rafael de la Llave
 KAM theory for quasiperiodic equilibria in 1D quasiperiodic mediaII: longrange interactions
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Jun 18, 12

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Abstract. We consider FrenkelKontorova models corresponding to 1 dimensional
quasicrystal with nonnearest neighbor interactions. We formulate and prove a
KAM type theorem
which establishes the existence of quasiperiodic 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
aposteriori 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
nondegeneracy conditions.
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