@article{Afzal2023, 
author = {Muhammad Afzal and Tariq Ismaeel and Azhar Iqbal Kashif Butt and Zahid Farooq and Riaz Ahmad and Ilyas Khan},
title = {On the reducibility of a class of almost-periodic linear Hamiltonian systems and its application in Schrödinger equation},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {7471-7489},
keywords = {Hamiltonian system, reducibility, almost-periodic, KAM method},
url = {https://www.sciopen.com/article/10.3934/math.2023375},
doi = {10.3934/math.2023375},
abstract = {In the present paper, we focus on the reducibility of an almost-periodic linear Hamiltonian system               d      X              d      t        =  J  [  A  +  ε  Q  (  t  )  ]  X  ,  X  ∈            R              2      d        ,where    J is an anti-symmetric symplectic matrix,    A is a symmetric matrix,    Q  (  t  ) is an analytic almost-periodic matrix with respect to    t, and    ε is a parameter which is sufficiently small. Using some non-resonant and non-degeneracy conditions, rapidly convergent methods prove that, for most sufficiently small    ε, the Hamiltonian system is reducible to a constant coefficients Hamiltonian system through an almost-periodic symplectic transformation with similar frequencies as    Q  (  t  ). At the end, an application to Schrödinger equation is given.}
}