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

Nina Xue, Wencai Zhao
2020 Journal of Function Spaces  
In this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system ẋ=A+εQt, where A is a constant matrix with possible multiple eigenvalues, Qt 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
more » ... me basic frequencies as Qt. Applications to the Schrödinger equation are also given.
doi:10.1155/2020/6260253 fatcat:cndu47ghqrcc3ioxxvntisbyqy