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      On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation

      1 , 2
      Journal of Function Spaces
      Hindawi Limited

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          Abstract

          In this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system x ̇ = A + ε Q t , where A is a constant matrix with possible multiple eigenvalues, Q t is analytic quasiperiodic with respect to t , and ε is a small parameter. Under some nonresonant conditions, it is proved that, for most sufficiently small ε , the Hamiltonian system can be reduced to a constant coefficient Hamiltonian system by means of a quasiperiodic symplectic change of variables with the same basic frequencies as Q t . Applications to the Schrödinger equation are also given.

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          Lectures on Celestial Mechanics

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            Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation

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              The one-dimensional Schr�dinger equation with a quasiperiodic potential

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                Author and article information

                Journal
                Journal of Function Spaces
                Journal of Function Spaces
                Hindawi Limited
                2314-8896
                2314-8888
                May 05 2020
                May 05 2020
                : 2020
                : 1-11
                Affiliations
                [1 ]School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China
                [2 ]College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China
                Article
                10.1155/2020/6260253
                4372d08d-2e25-4b81-9c71-8f1f90abf4ab
                © 2020

                http://creativecommons.org/licenses/by/4.0/

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