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

Author

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  • Hongwu Tang
  • Mingyan Xing
  • Qihuai Liu
  • Guirong Jiang

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 and , 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.

Suggested Citation

  • Hongwu Tang & Mingyan Xing & Qihuai Liu & Guirong Jiang, 2018. "On the Periodic Orbits of Four-Particle Time-Dependent FPU Chains," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-13, April.
    • Handle: RePEc:hin:jnlamp:4526917
    DOI: 10.1155/2018/4526917
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