# American Institute of Mathematical Sciences

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## On the reducibility of a class of almost periodic Hamiltonian systems

 a. School of Mathematics and Statistics, Xuzhou Institute of Technology, Xuzhou, 221111, China b. College of Mathematics, Southeast University, Nanjing, 210096, China

Received  October 2019 Revised  July 2020 Published  September 2020

Fund Project: The authors are supported by NSFC grant 11526177 and the Natural Science Foundations for Colleges and Universities in Jiangsu Province grant 18KJB110029

In this paper we consider the following linear almost periodic hamiltonian system
 $\dot{x} = (A+\varepsilon Q(t, \varepsilon))x, \; x\in R^{2},$
where
 $A$
is a constant matrix with different eigenvalues, and
 $Q(t, \varepsilon)$
is analytic almost periodic with respect to
 $t$
and analytic with respect to
 $\varepsilon$
. Without any non-degeneracy condition, we prove that the linear hamiltonian system is reducible for most of sufficiently small parameter
 $\varepsilon$
by an almost periodic symplectic mapping.
Citation: Jia Li, Junxiang Xu. On the reducibility of a class of almost periodic Hamiltonian systems. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020268
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