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On the Effective Reducibility of a Class of Quasi-Periodic Hamiltonian Systems

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Abstract

In this paper, we consider the effective reducibility of the following quasi-periodic Hamiltonian system

$$\begin{aligned} \dot{x}=(A+\varepsilon Q(t,\varepsilon ))x,~|\varepsilon |\le \varepsilon _0, \end{aligned}$$

where A is a constant matrix with different eigenvalues, \(Q(t,\varepsilon )\) is analytic quasi-periodic on \(D_\rho \) with respect to t. Under non-resonant conditions, by a quasi-periodic symplectic transformation, the Hamiltonian system can be reducible to a quasi-periodic Hamiltonian system

$$\begin{aligned} \dot{y}=(A^*(\varepsilon )+\varepsilon R^*(t,\varepsilon ))y,~|\varepsilon |\le \varepsilon _0, \end{aligned}$$

where \(R^*\) is exponentially small in \(\varepsilon \).

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Correspondence to Jia Li.

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The first author is partially supported by Natural Science Foundation for Colleges and Universities in Jiangsu Province grant 13KJD110009, and the talented person summit in Jiangsu Province grant 2013JY003. The second author is supported by NSFC grant 11371090.

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Li, J., Xu, J. On the Effective Reducibility of a Class of Quasi-Periodic Hamiltonian Systems. Qual. Theory Dyn. Syst. 14, 281–290 (2015). https://doi.org/10.1007/s12346-015-0157-9

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  • DOI: https://doi.org/10.1007/s12346-015-0157-9

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