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Equilibrium points and periodic orbits of higher order autonomous generalized Birkhoff system

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Abstract

Equilibrium points and periodic orbits of a higher order autonomous generalized Birkhoff system are studied by using qualitative methods of ordinary differential equations and the Liapunov center theorem. First, the equilibrium points and their properties are obtained from the equations of equilibrium points. Then, the characteristic roots of the Fréchet derivative C are obtained, and the type of equilibrium points of the system is verified. Finally, the existence theorem of periodic orbits is given by the Liapunov center theorem.

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Authors and Affiliations

  1. Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu, 476000, People’s Republic of China

    Xiangwei Chen & Yanmin Li

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  1. Xiangwei Chen
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  2. Yanmin Li
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Correspondence to Xiangwei Chen.

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Chen, X., Li, Y. Equilibrium points and periodic orbits of higher order autonomous generalized Birkhoff system. Acta Mech 224, 1593–1599 (2013). https://doi.org/10.1007/s00707-013-0810-9

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  • DOI: https://doi.org/10.1007/s00707-013-0810-9

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