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

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...

Full description

Saved in:
Bibliographic Details
Published inAdvances in Mathematical Physics Vol. 2018; no. 2018; pp. 1 - 13
Main Authors Jiang, Guirong, Liu, Qihuai, Xing, Mingyan, Tang, Hongwu
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2018
Hindawi
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Chains
Dynamical systems
Eigenvalues
Localization
Orbits
Physics
Time dependence
United States
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1687-9120
1687-9139
DOI:10.1155/2018/4526917