On the Periodic Orbits of Four‐Particle Time‐Dependent FPU Chains

Hongwu Tang, Mingyan Xing, Qihuai Liu and Guirong Jiang

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

Abstract: We study the existence of the periodic orbits for four‐particle time‐dependent FPU chains. To begin with, taking an orthogonal transformation and dropping two variables, we put the system into a lower dimensional system. In this case, the unperturbed system has the linear spectra 2 and 2, which are rational independent. Therefore, the classical averaging theory cannot be applied directly, and the existence and multiplicity of periodic orbits for four‐particle FPU chains is proved by using a new result from averaging theory by Buică, Francoise, and Llibre.

Date: 2018
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https://doi.org/10.1155/2018/4526917

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:4526917

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