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Reducibility for a Class of Nonlinear Quasi-Periodic Systems under Brjuno-Russmann’s Non-resonance Conditions

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Abstract

This paper studies the following analytic quasi-periodic nonlinear system

$$\begin{aligned} {\dot{x}}=(A+\varepsilon Q(t,\varepsilon ))x+\varepsilon g(t,\varepsilon )+h(x,t,\varepsilon ), \end{aligned}$$

where A is a constant matrix and \(h=O(x^2).\) We prove that under Brjuno-Russmann’s non-resonance conditions and non-degeneracy conditions, for most small enough parameter \(\varepsilon \), this nonlinear system is reducible by a quasi-periodic mapping.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xuzhou Institute of Technology, Xuzhou, 221111, People’s Republic of China

    Chunpeng Zhu & Jia Li

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  1. Chunpeng Zhu
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  2. Jia Li
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Correspondence to Jia Li.

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The work was supported by Natural Science Foundations for Universities of Jiangsu Province (18KJB110029).

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Zhu, C., Li, J. Reducibility for a Class of Nonlinear Quasi-Periodic Systems under Brjuno-Russmann’s Non-resonance Conditions. Qual. Theory Dyn. Syst. 22, 5 (2023). https://doi.org/10.1007/s12346-022-00702-x

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