Article Contents
Article Contents

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

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.

Mathematics Subject Classification: 37J40.

 Citation:

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