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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

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  • 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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