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    An extension of KAM theory to quasi-periodic breather solutions in Hamiltonian lattice systems

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    viveros_jorge_200712_phd.pdf (712.0Kb)
    Date
    2007-11-14
    Author
    Viveros Rogel, Jorge
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    Abstract
    We prove the existence and linear stability of quasi-periodic breather solutions in a 1d Hamiltonian lattice of identical, weakly-coupled, anharmonic oscillators with general on-site potentials and under the effect of long-ranged interaction, via de KAM technique. We prove the persistence of finite-dimensional tori which correspond in the uncoupled limit to N arbitrary lattice sites initially excited. The frequencies of the invariant tori of the perturbed system are only slightly deformed from the frequencies of the unperturbed tori.
    URI
    http://hdl.handle.net/1853/19869
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    • Georgia Tech Theses and Dissertations [22398]
    • School of Mathematics Theses and Dissertations [399]

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