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Twist character of the least amplitude periodic solution of the forced pendulum

Jinzhi Lei Tsinghua University Xiong Li Beijing Normal University Ping Yan Tsinghua University Meirong Zhang Tsinghua University

Classical Analysis and ODEs mathscidoc:1702.05005

SIAM J. MATH. ANAL., 35, (4), 844-867, 2003
In this paper, we will derive some twist criteria for the periodic solution of a periodic scalar Newtonian equation using the third order approximation. As an application to the forced pendulum x ̈ + ω^2 sin x = p(t), we will find an explicit bound P (ω) for the L1 norm, ∥p∥1, of the periodicforcingp(t)usingthefrequencyωasaparametersuchthattheleastamplitudeperiodic solution of the forced pendulum is of twist type when ∥p∥1 < P (ω). The bound P (ω) has the order of O(ω1/2) when ω is bounded away from resonance of orders ≤ 4 and ω → +∞.
forced pendulum, periodic solution, third order approximation, twist coefficient, twist character
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@inproceedings{jinzhi2003twist,
  title={TWIST CHARACTER OF THE LEAST AMPLITUDE PERIODIC SOLUTION OF THE FORCED PENDULUM},
  author={Jinzhi Lei, Xiong Li, Ping Yan, and Meirong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210172004078079432},
  booktitle={SIAM J. MATH. ANAL.},
  volume={35},
  number={4},
  pages={844-867},
  year={2003},
}
Jinzhi Lei, Xiong Li, Ping Yan, and Meirong Zhang. TWIST CHARACTER OF THE LEAST AMPLITUDE PERIODIC SOLUTION OF THE FORCED PENDULUM. 2003. Vol. 35. In SIAM J. MATH. ANAL.. pp.844-867. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210172004078079432.
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